Showing posts with label arrow's theorem. Show all posts
Showing posts with label arrow's theorem. Show all posts

Friday, 13 June 2025

Ken Arrow's argument for Socialism

Kenneth J. Arrow A Cautious Case for Socialism
The discussion of any important social question must involve an inextricable mixture of fact and value.

No. It must involve social facts i.e. intersubjective observables arising out of social processes. Those processes can be 'factorized' in terms of values, preferences, expectations, perceptions, Tardean and other mimetic effects, coordination and discoordination problems and so forth. 

Saying, 'it is a fact that one inch is equal to 2.54 cm and what I'd really value is a dick which wasn't just 2 point fucking 54 centi-fucking-meters long' is not the answer of any important social question though it may explain why my marriage failed.

The fundamental impulse to change and especially to great change is a perception of present wrong and a vision of potential right.

Nonsense! The impulse is to defend what you have or to grab what appears within reach. We may pretend otherwise but that's because we have no fucking shame. 

The initial impulse must still be checked for feasibility;

Evolution has already done that for us. Some will check for feasibility though they die or go bankrupt in the attempt. The fact is, all species, at the macro level, have a Hannan consistent strategy- i.e. there is some discovery and there is some hedging and redundancy.  

we live in a world of limits, and what we desire may not be attainable or it may be attainable only at the expense of other high values.

It's called 'opportunity cost' dude. Second rate mathematicians should not be allowed to become Economists because they don't know Econ and don't understand that not anything you call a set is a set nor is everything you call a function actually a function.  

There is an ancient warning, "Be careful what you dream of when young; your dreams may come true!"

Be careful of what you spend money or time on. Dreams don't cost anything. 

With the painter Braque, then, I can say, "I like the rule that corrects the emotion."

 What Braque liked was money. If he had to pretend he was a great artist to get it, so fucking what? 

But that presupposes a strong emotion to begin with;

Nope. A guy trying to flog his paintings or his poems isn't going to say he did it for the money and that he had one eye on the TV all the time. He's going to pretend to have deep emotions or spiritual insights or some such shite.  

and it is there I would like to begin. Values and emotions are best apprehended personally,

Or not. We pay good money to go to a Horror movie or Pop Concert. Indeed, a lot of people give substantial sums to their Church.  

and I will speak of my own attitudes and their development. This does not mean that my values are all that matter, even to me. I hold that others are free and autonomous human beings,

but they form expectations on the basis of what most other people's expect. This is not autonomy it is interdependence or impredicatitivity.  

each capable of developing his or her own value system of equal worth and respect to my own.

Not with respect to something important to you but not to her.  

But by that very token, the values of others must always retain an element of mystery.

We can guess at what they really are easily enough. Sadly, there are people who can make better guesses about what it is we really value than we can ourselves. When I was young, I thought I liked drinking beer. I didn't really, I just wanted to fit in with the other blokes. The truth is, I like girlie drinks 

The equal but different emotionally based axiological drives of others can never be fully communicated.

Who the fuck would want to listen?  

This is not to say that they. cannot be partly understood; historical study, sociological inquiry, intellectual debate, and the many dimensions of the political process are all ways in which we do communicate values. But my own values are the starting point, though not the terminus. In the oftquoted words of the sage Hillel,

who was a Rabbi. He got paid to do job and did it well.  

"If I am not for myself, then who is for me?" to which he immediately added, "and if I am not for others, then who am I?"

Not a Rabbi. You will have to find some other way to make a living. Alternatively, just lie about how much you care for others and for God and so forth.  

This methodological preface is by way of apology for the extent to which this paper is an intellectual autobiography. Notice the adjective, "intellectual." Anyone who knows me will not be surprised; I have always preferred the contemplative to the active life.

Contemplatively, I've just had sex with ten million super models all of whom were touchingly grateful. Actively- not so much. There's a good reason why many prefer the contemplative life.  

I prefer the freedom to see matters from several viewpoints,

e.g. the viewpoint of the millions of super-models I am bringing to orgasm

to appreciate ironies, and indeed to change my opinion as I learn something new. To be politically active means to surrender this freedom.

Nonsense! Politicians do U-turns all the time. What Arrow means is 'activism'- i.e. gesture politics and virtue signalling. But, they may as well make miaow miaow noises for any good they are doing.

I say nothing against activism for others. It is only through the committed that necessary changes come.

It is never through them.  

But each to his own path. The great issues of socialism and capitalism became alive to me, as to so many others, in the Great Depression.

There was no great issue. Countries which doubled down more on doing stupid shit suffered more than those which didn't.  Those which didn't, didn't. 

...Surely, a rationally organized, centrally coordinated economic system could avoid the instability of the capitalist economy

as could a capitalist economy. What matters is expectations. If people think they are going to be well rewarded, they are optimistic and active. But if the contagion of pessimism spreads then there is a Great, fucking, Depression. Socialism can work fine if the Dictator is doing sensible things and people expect that they will be shot in the head if they aren't joyously working their asses off. But this is also true of dudes who work for Al Capone. 

and the terrible human and material costs of unemployment.

as opposed to getting a lot of over-time at the Gulag.  

Further, there was such an economy. The Soviet Union was building and expanding, there was no unemployment, at a time when the advanced capitalist economies were spiraling downward or at best stagnating. The New York Times was the source of this favorable information, much more to be believed than the Communist party pamphlets passed out on the streets. To be sure, the Hearst newspapers were telling us about famine and repression in the Ukraine; but who would believe them? My family was hardly radical; indeed, they changed from Republicans

who cracked down on Ashkenazi immigration with the Johnson-Reed Act of 1924. 

to New Deal Democrats only under the influence of poverty.

Southern Democrats, like Breckinridge Long, were even more anti-Semitic. 

But the Hearst newspapers were not respectable; my unwillingness to trust them as against the Times had perfectly respectable middle-class justification. I have spoken so far as if efficiency were the main value. Indeed, it was true that the apparent sheer irrationality of the workings of capitalism was a basic condemnation.

Expectations, in a deeply divided Democracy, where some powerful people care more about maintaining relative privilege or waging class war than the absolute standard of living, are bound to be pessimistic. This is a country which is likely to do stupid shit. In Econ, expectations create reality. In Politics, perceptions are reality.

But as I observed, read, and reflected, the capitalist drive for profits seemed to become a major source of evil.

The evil of immigration? I suppose so. Europeans would never have immigrated to America if its capitalist drive for profits hadn't killed off the indigenous people.  

Clearly, the individualistic profit drive had something to do with the uncoordinated inefficiency of capitalism.

Markets coordinate activate. So do Cartels. Sadly, Hoover and Roosevelt supported Cartelization. Nobody gave a shit about allocative efficiency.  

But, more, the drive for profits had other manifestations. The Nye committee,

Nye blamed immigrant Jews for 'war mongering'. He was an America Firster. He found no evidence of a conspiracy of Capitalists to take America into the Great War.  

a congressional investigating committee, was engaged in a major investigation of the munitions industry; its influence over governments in creating the fears that improved its sales seemed to be well documented.

Only seemed. There was no evidence. Nye's mistake was to attack Woodrow Wilson. That led to a backlash.  

The economic explanations of imperialism were virtually standard.

Because Imperialism was dead and thus people could pretend it was actually an undead Vampire. Nobody dissed Count Dracula while he was alive because he was kicking Turkish ass. Incidentally, King Charles is related to Vlad the Impaler.  I hope he bites Sir Keir Starmer.  

Charles Beard and other historians had accustomed us all through their books to seeking an economic explanation of all political actions. The Constitution represented a certain set of economic interests, the Civil War a conflict, sometimes called "irrepressible," of different profit-seeking groups. Most serious of all, World War I, a tragic living memory, was clearly caused, at least in great measure, by competition among the capitalist interests of the different powers.

The Kaiser and the Tzar and the Caliph were actually Merchant Bankers. The Hapsburg Emperor, on the other hand, was the head of the Pork Belly Cartel. The King Emperor owned the biggest chain of Department Stores. Incidentally, he was a cousin of the Kaiser. Their common grandmother had started off selling flowers in Covent Garden. Her name was Eliza Doolittle. She made her fortune speculating in traded options.  

It was in this area of political-economic interactions that Marxist doctrine was most appealing.

appalling, more like.  

I was never a Marxist in any literal sense,

Nobody was. Marx literally was not a Marxist.  

unlike a great many of my fellow 473 students at the City College, in New York. Irving Kristol has written an evocative article on the intensity of intellectual life among the anti-Stalinist Marxists who foregathered in Alcove One and listed the many eminent social scientists and literary critics who emerged from this training. It would appear a Marxist background is an essential prerequisite for the development of a neoconservative thinker.

Nonsense! Being a cunt is qualification enough.  

I could not follow Marxist doctrine very literally for a number of reasons. The labor theory of value was a stumbling block even before I studied economics with any seriousness;

Values arise on coordination and discoordination games. One can value one thing in one way as part of a pooling equilibrium, while thinking it shit as part of a separating equilibrium. Knightian Uncertainty is the reason we live in a 'superimposed' state. Arrow ignored Knightian Uncertainty to write nonsense.  

there were too many obvious phenomena that it ignored. Nevertheless, the insight Marxist theory gave into history and particularly as to political events was striking: the state as the executive committee of the bourgeoisie,

rather than a bunch of megalomaniacal gangsters 

the class interpretation of political and social conflicts, and the interpretation of war and imperialism as the conflict of competing national capitalist interests were illuminating and powerful.

They were fucking obvious. Imperialists kept saying 'we need to grab those resources or markets'. The problem was that it was seldom profitable to do so. The trick was to get the costs to fall on the tax-payer, wile the profits were monopolized by a bunch of cronies.  

It appeared more profound than the alternative versions of the economic interpretation of history; they seemed to be mere muckraking, the behavior of venal individuals.

People can decide certain markets are repugnant- e.g. prostitution, 'sweated labour', slum landlordism- and laws can be passed to curb such activities. 

Marxism put the system rather than the individual into the foreground.

The problem was that individuals- e.g. Stalin or Trostsky- would be in charge of changing the system. They might decide to kill you because you were a 'right deviationist' or a 'left adventurist' or might turn into some such thing one fine morning.  

What I drew from this thinking was an argument for system change.

Systems, like individuals, change over time. I suppose, if one group of people achieves absolute power by killing all its enemies, then it can impose any system it likes.  

The basic criterion for change was moral and ethical. I did not accept ideas of historical inevitability. What the Marxist analysis did say to me, at least then, was that the system of production according to profit established vested interests in destructive activity,

Pigouvian taxes or outright bans would take care of this problem. 

most especially war and imperialism,

During the inter-war years, it did seem that gun-salesmen like Sir Basil Zaharoff were trying to start wars. 

but also oppression of workers and destruction of freedom. I do not believe I ever accepted the theory that racial discrimination was the result of capitalist endeavors to divide the working class,

Dark skin is a costly to disguise signal and can be used for wage, price and service provision discrimination. The same is true of gender.  

but I certainly accepted the general belief that the capitalist class would overthrow democracy rather than lose its power, as it had done in Italy and Germany

the capitalist class lost power to the Il Duce & the Fuhrer. So did everybody else.  

and was then striving to do in Spain.

Raping nuns was a bad idea. There was bound to be a reaction.  

Thus, beside the efficiency value, the values of freedom and the avoidance of war were vital in my attitude toward socialism.

The problem was that avoiding war may mean appeasement and then war occurs anyway.  

The two were and are intimately linked in my mind. Being killed is, after all, a rather extreme form of deprivation of freedom, and in a typical modern war, the killer is subject to as much compulsion as the killed. I tended therefore to a rather pacifist position. This position, to be sure, began increasingly to separate me from a revolutionary socialist position. On the value of freedom, I don't think I ever thought it through; it was just a value that was taken for granted.

It was costly to maintain a system of checks and balances.  

Obviously, an American education inculcates such a value strongly. However, I was naive or conscientious enough to take it very seriously and to be shocked at examples of its denial. Discrimination against blacks—denial of their political rights, segregation in housing and employment—was the most blatant case domestically; remember that lynching still existed. Imperial control of the United States, as in the Philippines, and, much more extensively, by Great Britain in India and Africa, served to demonstrate that political freedom had narrow limits under capitalism.

Imperialism isn't capitalism. 

The freedom of workers seemed to me much restricted. Strike-breaking by fairly direct and brutal methods, as well as more subtle forms of economic pressure, was a common event. Even apart from overt conflict, the regular operation of the factory appeared as a form of regimentation and a denial of individual freedom an implication then widely accepted, expressed in such movies as Chaplin's Modern Times and Rene Clair's A Nous La Liberte' and, more subtly and profoundly, in Lewis Mumford's Technics and Civilisation, then very famous and still worthy of rereading.

Ford had raised his workers' wages to a level where they could themselves buy the cars they produced. Hoover was keen on cartelization so as to remove the incentive for 'sweating labour'. FDR went further in that direction. The problem was Expectations. Recovery from the Depression was weak and could be reversed. It wasn't till re-armament on a massive scale that the US came out of the Depression. Was this some sort of trick? That was the question.  

A broader and less direct form of control flowed from the concentration of control in American industry, indeed capitalist industry everywhere. The importance of relatively few large industrial and financial corporations did not need much documentation, and numerous investigations documented their scandals. But massive support for the more scholarly minded came from Berle and Means's The Modern Corporation and Private Property, which established not merely the concentration of the productive sector into large firms but also the concentration of control within those firms. Even the capitalist stockholders were deprived of power, if not wealth.

There was a divorce between ownership and control. Perhaps, this meant that Socialism could be established by the back door. The Executive could deal directly with a cartelized industry. This was like the Corporatism seen in Fascist countries.  

The absorption of the economy by a small elite implied that the formal democracy and freedom was increasingly a sham; the major decisions on which human welfare depended were being made by a few, in their own interests.

The Government could pressurize them to become its lackeys.  

The same process had another implication, as Marx had argued long before; production was in effect already being carried on in socialized enterprises, so that the shift to a completely socialist economy would be that much easier.

This is the germ of the 'convergence hypothesis'. Capitalism and Socialism would become indistinguishable. There would be 'administered pricing'. The economy would feature 'fix-price' rather than 'flex-price' such that markets did not clear. There would be either unemployment or 'repressed inflation' (i.e. shortages). 

As some of my examples indicate, I did not find any sharp line to draw between the values of freedom and of equality. The typical example of lack of freedom was a great inequality of power. Much is made these days of the alleged opposition of freedom and equality; but I would have regarded the two as close to identical in many contexts. As for inequality of income, I took it for granted that it would be reduced under socialism by the abolition of the income category of profits.

In other words, the entrepreneur would be replaced by a salaried manager. The problem was that the managerial class might award itself perks while doing less and less work. The same problem arose with a 'nomenklatura' in a Socialist state.  

Finally, there was a strong antipathy to an economic and social system based on selfish and competing motivations. I eagerly sought confirmation in the works of contemporary anthropology, such as Margaret Mead's Sex and Temperament in Three Primitive Societies, for the proposition that cooperation was at least as natural as competition.

Sadly, peaceful cooperation may mean your society gets conquered by those who went in for military competition.  

My pacifist views coincided in a natural way with these broader motivational assumptions. Like many others of the time, I was strongly attracted by Gandhi's nonviolent campaigns against British rule.

Which failed.  

The underlying assumption was the common humanity of ruler and ruled; the appeals to cooperative and altruistic motives seemed to have at least some success as against the simple selfish exercise of power.

Westminster didn't want to waste its time passing laws for India. They had already made their settler colonies self-administering and self-garrisoning. Could India be turned into a Federation like Australia or Canada? No. The country would be divided on the basis of Religion as Ireland was divided.  

To sum up, the basic values that motivated my preference for socialism over capitalism were (1) efficiency in making sure that all resources were used,

How? The Socialist government may accept that there must be a minimum wage. But it may not be able to employ everybody at that pay-rate. There would be 'disguised unemployment'.  

(2) the avoidance of war and other political corruptions of the pursuit of profits,

It is not profitable to start a war you are bound to lose.  

(3) the achievement of freedom from control by a small elite,

A large elite isn't an elite. Either the thing is small or it does not exist.  

(4) equality of income and power,

in which case there is no incentive to shift to more efficient methods. Also, why be a plumber when you can be a party hack? Plumbing is a messy business. Attending committee meetings is a pleasant enough way to pass the time.  

and (5) encouragement of cooperative as opposed to competitive motives in the operation of society.

I encourage people to cooperate with me by doing my washing up. Also, some light hoovering.  

From the perspective of greater education and experience and with 40 years of history, my understanding of the relation between these values and the desirability of socialism has altered. Many countervailing considerations have been raised by further analysis and knowledge of the facts. One problem that I did not face was highlighted by history almost immediately. If capitalism was to be reprehended for its concentration of control and consequent inequality of power and lack of freedom for the average man, what would happen under socialism? Did not state ownership imply or at least permit overwhelming concentration of power in the hands of a political elite? Soviet Communism pushed these questions into our consciousness. For me, the Moscow trials of 1935-36 were a dramatic, even traumatic turning point.

I suppose there were board room coups of a similar type. The difference was that nobody got shot.  

It was clear that the old Bolsheviks were unjustly convicted, and their confessions only increased the horror, since it spoke of barbaric pressures.

The Soviets had created famines and slave labour camps. Barbarism is too kind a word. 

I reflected, too, that in the improbable event that the charges of treason were true, the Stalin regime was equally condemned; for what could induce those who had risked all under the Czars to create this new world to turn against it save a deep sense of its evil? However the facts were interpreted, they were not compatible with the idea that the Soviet Union was a democracy or was even moving in that direction. Differences of opinion, even among socialists, were not being tolerated. I had not believed that the Soviet Union was a genuine democracy at any time, but its political backwardness could easily be explained by history and the ring of quite genuine enemies it had.

Stalin rid the Kremlin once and for all of an uprising of Cossacks and agricultural labourers. He had escaped from Siberia many times. Under his rule, the whole country was a prison camp. There was nowhere you could escape to within the country.  

But now it appeared that as the generation raised under socialism came to adulthood and as the Soviet Union grew stronger vis-a-vis its enemies, the repression grew greater, not less. The true enormity of the Soviet tyranny was revealed only in time. But from my point of view, the challenge to socialism was already reasonably clear. At a minimum, the socialist economy did not guarantee democracy and individual freedom.

Or food. There had been big famines under Stalin.  

I had the naive idea that in the absence of a profit-making class, there would be no class interested in achieving power over others. It became clear that this view was hardly adequate. The worse problem was the possibility that socialism, by concentrating control of the economy in the state apparatus, facilitated authoritarianism or even made it inevitable.

Either you have incentives- e.g. more money for working harder- or you have penalties- getting shot for not overfulfilling your work quota. To be fair, the Soviets did believe in 'work measurement' and would reward 'Stakhonovites'.  

I return to this vital challenge below. I became seriously interested in the study of economics only after beginning graduate study around 1940.

Arrow was witnessing the creation of a massive military-industrial complex. Suddenly, the US had 'price czars' like John Kenneth Galbraith who was only 13 years older than Arrow.  

Needless to say, learning something of the workings of the economic system and of the logic of neoclassical economics had a considerable effect on my attitude toward socialism. George Stigler remarked once that the study of economics is a highly conservatizing force.

What is even more conservatizing is having to make a budget and stick to it. That's why Mummy is so strict.  

To some extent this is true, but only to the extent that any increase in knowledge may lead to greater realization of limitations. The inner coherence of the economy, the way markets and the pursuit of self-interest could in principle achieve a major degree of coordination without any explicit exchange of information—in short, the valid elements in Adam Smith's doctrine of the invisible hand—became important possibilities that qualified a simple view of the inefficiency of markets.

The price mechanism is only one of many coordinating mechanisms. The existence of hedging and income effects will cause allocative efficiency or render the general equilibrium 'anything goes'. The wider problem is Knightian Uncertainty which dictates a regret minimizing, rather than expected utility maximization, approach.  

Similarly, the facts of long-term economic growth in spite of the contemporary economic debacles had to register—though, to be sure, one could scarcely ask for a greater testimonial to the creative power of capitalism than was already contained in the Communist Manifesto. My immediate reaction was to interpret neoclassical economic theory and particularly the then new and rapidly developing discipline of welfare economics

which is merely the handmaiden of Public Finance. First figure out how much tax revenue you can raise and then decide how to spend it so as to create a virtuous circle such that Income and hence tax revenue rises more than proportionally.  

as pointing to an ideal efficient economy rather than the actual one, marked both by massive unemployment and by monopolistic distortion. Socialism was the way in which the ideal market was to be achieved. This doctrine was held by many, including especially the professor here at Columbia to whom I owe so much, both intellectually and personally, Harold Hotelling.

Hotelling had a great interest in Henry George's ideas- as did Vickrey. Stiglitz and others developed the 'Henry George theorem'. The European Left was suspicious of it. 

Graduate education in economics at Columbia at that time, just before our entrance into World War II, seemed curiously designed to emphasize the ideal nature of neoclassical theory. The dominating voices, Wesley Mitchell, J. M. Clark, and Arthur F. Burns, held that neoclassical theory had little descriptive value. Though Clark and Burns, at least, certainly had no support for socialism, their views, when taken into conjunction with the theorems of welfare economics, resonated with my convictions that socialism could yield a more efficient economy.

What would the incentive be for a Socialist planner to focus on efficiency rather than something more crowd-pleasing?  

Finally, the development of Keynesian economics and, after the war, its gradually increasing application changed the nature of the efficiency discussion. In true Hegelian fashion, capitalist instability and the socialist counterattack seemed to be synthesized: it seemed possible to have an economy that retained much of capitalist drive and initiative and yet gave room for the government to intervene to avoid at least the worst inefficiencies of unemployment and the idling of other resources.

Governments can certainly act in the public interest to restore business confidence and create a 'virtuous circle' whereby Income, and hence tax revenue, rises.  

I accepted provisionally what seemed to be a widespread consensus in the euphoria of postwar economic growth. The state had an active role to play in maintaining effective demand and in dealing with the many imperfections of the market system revealed by theoretical welfare economics— the overcoming of market failures and monopoly and the realization of economies of scale. These interventions should take the form of relatively impersonal measures, taxes and expenditures, rather than detailed controls and direct regulation.

More particularly because of the problem of 'Agency capture'. The industry under regulation might gain control over its supposed regulators.  

The higher taxes meant that the government was automatically engaged in redistributing, and some of us felt that it should go much further.

The problem was 'disutility'- i.e. opportunity cost or transfer earnings. This rises for employed people if unemployed people have a good enough standard of living. Welfare Econ never really came to grips with this problem.  

I have spoken of a provisional acceptance. I still felt it important to explore more deeply the possibility that socialism was a superior possibility. I was more aware of the complexities of operation of a socialist system and sought to develop more deeply the theory of such a system.

The USSR didn't really have a theory. It just had a pragmatic 'material balances' approach. The problem was quality control. On paper, you have exceeded your quota of widgets. But half the widgets are not fit for purpose.  

I also sought to explore more fully the criteria for a democratic social organization.

This is done by electing representatives, not by aggregating preferences.  

These matters could be thought of as matters for slow reflection and long-term analysis, so long as the economy seemed to be performing so well and the political process seemed to be responding, however slowly, to demands for improvements in efficiency, redistribution, and the overcoming of market defects. The apparent pause in economic growth, the crisis in stabilization policy occasioned by the current inflationary threats and realities, and the loss of purpose in redistributional measures all combine to raise anew the question of alternatives to capitalism.

What was sought was an alternative to the Bretton Woods' strait-jacket so that former colonies or protectorates could get a better deal for selling their petroleum. Finally, the Soviets realized that they too could have higher standards of living if they sold their petrol at world prices rather than subsidising their allies. 

In many of our sister democracies, the issue is much more closely on the agenda than it is here. Beyond that there is the large fraction of the world where socialism and authoritarianism coexist in varying degrees of comfort. And then, since, to twist a phrase of Marx's, every historical phenomenon appears as both tragedy and farce, we have the widespread solemn use of the word "socialism" to cover some of the most absurd travesties of that term.

North Korea had adopted the hereditary principle such that the Dictatorship of the Proletariat meant the ruler would be the son, grandson, or great grandson of the 'Beloved Leader'. 

Let me spend the remaining time in reexamining briefly the case for socialism from the viewpoint of the five values mentioned earlier: efficiency,

minimizing 'disutility' or 'opportunity cost'. Older people thought disutility was directly linked to the job whereas it is linked to the best alternative to the job. Suppose I get paid one million dollars a month to make love to super-models. I feel very happy. Then I hear you get paid two million for doing the same job. Suddenly, I feel very sad and hard done by.  

separating political decisions from selfish economic interests,

I unselfishly decide that your salary should be cut. You quit work. My political decision harms the economy.  

freedom,

costs money to maintain. It doesn't come for free as the Ukrainians can testify. 

equality of income and power,

everybody starving together 

and the stress on cooperative as against individualistic motives.

We have an individualistic motive to cooperate.  

These are not balanced remarks; only the favorable side will be presented. Perhaps on another occasion I will present the contrary case. The case for socialism from each value viewpoint is much more refined and complex than I originally thought, and there are many qualifications that must be made. But I still consider that the argument can be made. For reasons of time, I will deal only briefly with the last two points. With regard to equality of income, let me first remark that I am taking it to be a good, other things being equal.

Why not take equality of height and weight to be a good thing, ceteris paribus? Some people may want more income. Some may want more leisure. At different times in our life, our preferences in this respect change.  

It can be objected that the drive for equality may dull incentives, and the net result will be a reduction in everyone's real income. This is a legitimate instrumental objection but not an objection to the value presumption in favor of equality as such.

It is both. Values are instrumental. People with good values tend to do well. Equally, values which cause you to do badly are considered bad. At a time of peace and prosperity we may say that people who devote themselves to prayer have good values. Then the country is invaded. Those who merely pray are useless. Those who fight back can save the country.  

Many current thinkers object to distributive equality on principle, on the grounds that it contradicts freedom of property.

One may go further and speak of property ownership as an 'uncorrelated asymmetry' which dictates an eusocial 'bourgeois strategy'.  

This is a large subject; I simply state my conviction that property is itself a social contrivance

It may be. It may not. Animals behave in a territorial manner. That's a bourgeois strategy. 

and cannot be taken as an ultimate value, indeed, that institutions that lead to gross inequalities are affronts to the equal dignity of humans

which is a 'social contrivance'. I suppose, in law, there is some such notion. But does it exist in society? Is a homeless lunatic really of equal dignity to the President of the Republic?  

and can only be accepted as necessary evils.

Gravity is a necessary evil. I hope President Trump will ban it. 

It certainly seems as obvious as can be that a socialist economy can achieve much closer income equality than a capitalist economy.

So can a hunter-gatherer society. Let us ban agriculture and industry.  

The category of profits is absent.

i.e. you can't sell any turnips you happen to grow.  

While we now understand that most inequality in income is due to inequality of so-called labor incomes, it is certainly true that the ability to acquire profits increases inequality.

It also enables retired people to have a decent standard of living. Getting rid of profits means your pension fund gets no dividend income and thus can't pay your pension. 

Further, the higher end of the income of professionals and executives is largely a rent in the economic sense and would be unnecessary in a socialist society.

Because the nomenklatura don't wear clothes or require expensive apartments and limousines.  

One needn't ask for utopian dreams of virtually complete equality of income.

One can be grateful that the 'Beloved Leader' is building himself another Palace.  

In a world of any complexity, there must necessarily be both antagonistic and cooperative elements. The model laissez-faire world of total self-interest would not survive for ten minutes; its actual working depends upon an intricate network of reciprocal obligations, even among competing firms and individuals. But the capitalist system is structured so as to minimize cooperative endeavor.

Coase's theory of the firm suggests it exists to internalize externalities. There is a lot of cooperation within it.  

The worker is a factor of production, a purchased item, not a part of a team.

No. He is a part of a team and his emoluments may reflect his seniority or his loyalty and cooperative spirit.  

The attempts to handle externalities in recent years have led to interesting resistances; antipollution regulations are perceived as a threat to profits, not a social gain.

They move pollution to poorer areas. The affluent gain better air quality. The poor choke.  

Again, socialism is far from a magic cure. Each suborganization, for example industrial plants, will have its own proximate goals, which will not mesh completely with those of others. But the system should permit a greater internalization of broader goals. It should be easier for a plant to regard product safety as one of its socially valued outputs.

The leading cause of fires in Moscow, at around that time, was exploding TV sets. Socialism may not bother with product safety. A private company whose products keep exploding will soon go bankrupt.  

The comparative economic efficiency of capitalism and socialism remains one of the most controversial areas. The classical socialist argument is that the anarchy of production under capitalism leads to great wastage.

In which case a new manager can boost profit by cutting down on waste.  

An appeal to the virtues of the price system is, in fact, only a partial answer to this critique. The central argument, which implies the efficiency of a competitive economic system, presupposes that all relevant goods are available at prices that are the same for all participants and that supplies and demands of all goods balance. Now virtually all economic decisions have implications for supplies and demands on future markets. The concept of capital, the very root of the term "capitalism," refers to the setting-aside of resources for use in future production and sale. Hence, goods to be produced in the future are effectively economic commodities today. For efficient resource allocation, the prices of future goods should be known today. But they are not.

Which is why some arbitrageurs will specialize in making better predictions of what they will be. These 'market makers' should smooth out prices and reduce the burden of uncertainty on other agents.  

Markets for current goods exist and enable a certain coherence between supply and demand there. But very few such markets exist for delivery of goods in the future.

This is true of any economic system.  

Hence, plans made by different agents may be based on inconsistent assumptions about the future.

This is true of any kind of plan. People get married thinking that their spouse shares the same plan for the future. Then it turns out the spouse's plans is to fuck anything that moves while spending money like a drunken sailor.  

Investment plans may be excessive or inadequate to meet future demands or to employ the future labor force.

This is also true of a family of shepherds. They may not have enough sheep to remain in that employment. Sooner or later some of the sons have to get jobs in a factory or a coal mine or join the army.  

The nonexistence of future markets is no doubt linked to uncertainty about the future.

There is no 'market maker' for it because it is not profitable. Still, contracts of this type can be made even if there is no 'clearing price'.  

But this points to an even more severe shortcoming of the actual capitalist system compared with an ideally efficient economic system.

Actual things have shortcomings relative to ideal things. 

The uncertainties themselves are relevant commodities and should be priced in such an economy. Only a handful of insurance policies and, to a limited extent, the stock market serve to meet the need for an efficient allocation of risk-bearing.

It is efficient only if ex ante expectations match ex post outcomes. But this is true of any type of activity. I am pressing buttons on my TV remote. Nothing is happening. Why? Oh. I have to replace the batteries. I was behaving inefficiently by shouting at the TV and cursing the remote control.  

In the ideal theory of the competitive economy, market-clearing prices serve as the communication links that bring into coherence the widely dispersed knowledge about the needs and production possibilities of the members of the economy.

Some 'open markets' do clear well enough. Sometimes 'market-makers' with expert knowledge can improve outcomes. Sometimes irrational speculation can worsen matters.  

In the absence of suitable markets, other coordinating and communicating mechanisms are needed for efficiency.

Why not scold the economy till it becomes sweet and nice?  

These come close to defining the socialist economy, although admittedly wide variations in the meaning of that expression are possible. As I have already suggested, the existence of idle resources is a prime example of coordination failure.

A more striking example is vast numbers of people starving to death. Being idle is better than being dead.  

The experience of the Communist countries bears on this point.

They had big 'man made' famines. The result was that the regime no longer had to fear an uprising of the peasants.  

With all their difficulties and inefficiencies, and they are not few, recurrent or prolonged unemployment is not one. A graph of economic activity in the United States is, under the best of circumstances, jagged and spasmodic, that of the Soviet Union much smoother.

If you make up the figures, your graphs will be smoother.  

Fluctuations there are, as there must be in any complex dynamic system.

Life is an example of such a system. We can't remain babies forever.  

But the planning, however inept, serves to keep the basic resources and their uses in line.

So does slavery.  The problem with both Communism and Slavery is that workers keep running away. 

The sophisticated antisocialist reply to this argument is not to deny it but to emphasize that a socialist system is not an ideal resource-allocating mechanism either.

The difference is that you can directly change preferences by shooting people.  

Much is made of the obvious inefficiencies of the Communist countries, though the Soviet growth rate and technical development has on occasion caused fear and trembling and overall still averages above the United States rate.

Which is why so many Americans were running away to the USSR. It wasn't the case that the Berlin Wall was designed to prevent people fleeing to the Capitalist West.  

As all too frequently happens in the social sciences, no clear-cut dominance pattern of efficiency can be found either way.

But you could look to see what was happening at the margin. Did people run away from the USSR to the USA or vice versa?  

All that can be said is that socialism is clearly a viable economic system, contrary to what many would have asserted in the not-too-distant past, and it does not release energies and productivity far beyond the capitalist norm.

There were periods when Communist countries seemed more energetic. There were some remarkable Soviet mathematical economists. The big question was whether Kantorovich's vision could be realized using networked computers. In the early Seventies some believed this was possible.  

I have referred rather vaguely to the corruption of the political system by narrow economic interests as one of the evils of capitalism that might be avoided under socialism.

Where you could have just plain and simple corruption. Brezhnev's daughter was supposed to be very corrupt. Still, I suppose it was the post-Yeltsin plutocrat who made much bigger fortunes.  

More explicitly, a democratic polity is supposed to be based on egalitarian distribution of political power. In a system where virtually all resources are available for a price, economic power can be translated into political power by channels too obvious for mention.

But plutocrats may compete with each other for that political power. Some will seek to ally with organized Labour so as to score over their rival.  

In a capitalist society, economic power is very unequally distributed,

whereas, under Socialism, babies are just as productive as skilled engineers.  

and hence democratic government is inevitably something of a sham.

Why are there so few babies in the Senate? It is because Democracy is a sham.  

In a sense, the maintained ideal of democracy makes matters worse, for it adds the tensions of hypocrisy to the inequality of power. My early assumption that only capitalists would have an incentive to influence democratic decisions was too simple. Everyone in an economy has an economic interest. It is also true that individuals have interests and attitudes that do not derive from their economic improvement and may even oppose it. But it is today a widespread doctrine, held by conservatives as well as socialists, that concentrated economic interests are more than proportionally powerful in the political process.

The problem is that they may overplay their hand 

George Stigler and his colleagues have maintained with great vigor that regulation of industries is usually carried out in the interests of the regulated and is not infrequently originated by them.

There was also the problem of the Government stockpiling and sitting on patents. People in the Tech industry felt that innovation was being held back by a bureaucratic cabal.   

The reasons offered are perfectly in accordance with ordinary economic principles; there are economies of scale in the political process, so that a small economic interest for each of a large number of individuals is less likely to get represented than a large interest by a small number.

The emergence of tax-exempt Political Action Committees could bypass the established political parties by backing those who would promote their agenda regardless of party affiliation.  

So long as the state power can be democratically run, much of this distortion of the democratic process should be minimized under socialism.

Socialists have their own 'sacred cows' and want more to be spent on wasteful schemes which signal their commitment.  

Income inequalities should be greatly reduced.

In which case, why become a plumber rather than try to make it big as a pop star?  

Economic power deriving from managerial control rather than income should be less easily translatable into political power than under a regime of legally and practically autonomous corporations.

The Medieval Church had a lot of 'managerial control' because it owned vast estates and monopolized higher education and the higher ranks of the bureaucracy. This meant it had great political power. It could even excommunicate the King.  

We come then, finally, to what is probably the most serious of all the concerns about socialism. Is it in fact compatible with freedom and democracy? It is the fear that socialism may bring tyranny that has inhibited so many of us from being more active advocates.

Communism had brought tyranny. The British Labour Party had not done so. 

It is noteworthy that when Joseph Schumpeter wrote on Capitalism, Socialism, and Democracy, he affirmed that socialism, which he thoroughly disliked, was fully compatible with political democracy.

This was obvious to the English. Working class Members of Parliament did not want to replace Capitalist tyranny with the tyranny of Cambridge educated Commissars.  

It is only perhaps with Friedrich von Hayek's The Road to Serfdom that the association of capitalism and democracy became a staple of the procapitalist argument. The association itself, however, was not new; it was one of the standard Marxist views, though not held by all. The hypothesis was that the resistance of capitalists to the coming of socialism will lead to the subversion of democracy by them. At least the transition will require the "dictatorship of the proletariat," a phrase whose ambiguities have been only too well clarified by history.

Trotsky did create a Red Army which was able to defeat the Whites and extract surpluses from the peasants.  

This Marxist view indeed gives credit to capitalism for the origins of democracy; it is an appropriate political form, a parallel to the ideas of free contract. So long as the "contradictions" of the system are not too sharp, the nominal equalization of political power offers no threat because economic power is so preponderant. But democracy will decline with the failure of capitalism.

If there are no profits, what is the incentive for investment? The fixed capital of the country will depreciate and become useless. Standards of living will fall.  

The experience of Chile, to cite only a recent example, certainly gives some credence to this theory.

There was a CIA backed coup. Chile was unusual in many respects. It has been suggested that Allende hadn't won convincingly and thus didn't have a mandate for implementing quite a radical program. I suppose, the truth is Chile was badly affected by the fall in the price of copper. It is said that the US supplied funds to strikers with the aim of paralysing the regime. The Soviet bloc and China did give some assistance but they may have been sceptical as to whether Allende had the stomach for the sort of tough action needed to stay in power. 

Ironically, the current conservative model explaining the supposed association of capitalism and democracy relates to the Marxist as a photographic negative to a positive. It too suggests that the political "superstructure" is determined by the "relations of production."

Graciella Chichinlisky, from Argentina, suggests that Democracy is problematic if there is too great preference and endowment diversity.  

The conservative model contrasts the dispersion of power under capitalist democracy with its concentration under socialism.

Dornbusch spoke of Allende's 'macroeconomic populism'. The problem was that he could not control the supply side. Maybe if copper prices had been booming, he'd have remained in power as a beloved benefactor to the Chilean masses.  

Political opposition requires resources. The multiplicity of capitalists implies that any dissenting voice can find some support. Under socialism, the argument goes, the controlling political faction can deny its opponents all resources and dismiss them from their employment. This theoretical argument presupposes a monolithic state. It is something of a chicken-and-egg proposition.

If Socialism means social control of the means of production, then the ruling party would have a monopoly. But, there would still have to be production. If production is falling while the State raises wages and freezes prices, you get 'repressed inflation'- in other words goods disappear from the market. 

If the democratic legal tradition is strong, there are many sources of power in a modern state. Adding economic control functions may only increase the diversity of interests within the state and therefore alternative sources of power. It is notoriously harder for the government to regulate its own agencies than private firms.

Surely, that's the clinching argument against Socialism?  

Socialism may easily offer as much pluralism as capitalism. The overpowering force in all these arguments is the empirical evidence of the Soviet Union and the other Communist countries, and it is strong.

Gulags are very plural.  

But the contrary proposition, that capitalism is a positive safeguard for democracy, is hardly a reasonable inference from experience.

A democracy may decide that the only way it can survive is to grab land and resources from its neighbours.  

The example of Nazi Germany shows that no amount of private enterprise prevents the rise of totalitarianism.

The Weimar Constitution permitted the President to rule by decree.  

Indeed, it is hard to see that capitalism formed a significant impediment.

Capitalists had read Keynes's 'Economic consequences of the Peace'. Keynes said the US was becoming a net food importer. Britain and France and Holland and Belgium would be fed by their colonies. The Germans would starve unless the grabbed land from their Eastern neighbours. Hitler was brought into politics by the German Army. He only became Fuhrer because Ludendorff was barking mad.  

Nor is Nazi Germany unique; Fascist Italy, Franco's Spain, and the recurrent Latin American dictatorships are illustrative counterexamples to the proposition that capitalism implies democracy.

Anglo Saxon polities are democratic. Latins aren't. An 'enlightened despot' may sponsor Capitalism. Dubai is Capitalist. Democracy might destroy its prosperity.  

Further evidence can be drawn from the increasing role of the state in guiding economic activity. The United States, the United Kindom, and Sweden, though not socialist as that term is properly used, have certainly greatly increased their intervention in the economy.

They began to scale this back as 'stagflation' took root.  

Yet democracy and political and personal freedom have never been stronger in these countries.

Bertrand Russell would disagree. When he was young he could travel anywhere and buy and sell virtually anything he liked. In old age, he was subject to Exchange Control. Americans were in a worse position. They couldn't even own gold.  

Indeed, Samuel Huntington has argued that an excess of democracy makes it difficult to meet the current problems of the United States.

Nobody could understand America's 'twin track' energy policy. Many other government schemes were equally opaque.  It was discovered that candidate Reagan did not understand agricultural parity prices. People were ready to laugh at him. Then they ruefully realized that nobody understood the thing.

The evidence, it seems to me, points to the view that the viability of freedom and democracy may be quite independent of the economic system.

During the War, Arrow had seen the US transformed into a Command Economy. Then it reverted, at least partially, to a Capitalist system. Nixon was the first and last avowed Keynesian. What would come next? Few thought it would be Reagan.  

There can be no complete conviction on this score until we can observe a viable democratic socialist society.

Maybe one with 1.8 trillion in its National Wealth fund- like Norway. The problem is that entrepreneurs may run away. 

But we certainly need not fear that gradual moves toward increasing government intervention or other forms of social experimentation will lead to an irreversible slide to "serfdom."

The Tzar had to get rid of 'serfdom'. It was uneconomic. Ultimately, countries have to compete with each other. If the US has nukes, the Soviets have to get nukes. If the Soviets have Sputnik, the Americans have to get Apollo. The reality was that Arrow had been paying taxes so as to ensure that an American President could press a button and blow up the world. This was not the irenic, idealistic, world of the inter-war period. It was foolish to talk of Capitalism and Socialism and Democracy when these political systems ultimately depended on a nuclear button and 'mutually assured destruction.'  

It would be a pleasure to end this lecture with a rousing affirmation one way or the other. But as T. S. Eliot told us, that is not "how the world will end."

If the world ended, it would be because of nuclear war. Dr. Strangelove would be the only winner.  

Experiment is perilous, but it is not given to us to refrain from the attempt.

Is Democracy compatible with a 'National Security State'? Sure, if your President can blow up the world. This was not the earlier view. Democracy required some collective method of preventing war. On the other hand, Total War had led to a fundamental change in the nature of the State and the distribution of 'control rights' within it. In a sense, the affluent society with its increasing range of liberties was the reward for having at its disposal the possibility of mutually assured destruction. But this meant that the luxuries enjoyed on one side of the iron curtain, was mirrored in the privations experienced on the other side as the weaker economy strove to catch up in terms of nuclear bombs and delivery systems. 

Friday, 30 May 2025

Why Social Choice theory failed

 How does a Society decide on what it should do? The answer, in a Democracy, is that it chooses particular agents and entrusts those agents to decide on certain matters. Some of those agents may be chosen through elections. Others may have specific skills and may have risen through merit or seniority. There are five main types of decisions and each has different types of agents in charge of decision making.

1) There is an Executive which decides matters of general fiscal, monetary, military and diplomatic policy. The Chief Executive may be directly elected or may be chosen by Parliament or, during periods of Emergency, be appointed because of some special expertise or popular reverence that they enjoy. 

2) there is a Legislature which passes laws and approves the budget. Some portion of it may be directly elected and some may be nominated or belong by hereditary right. 

3) there is a Judiciary which is, at least notionally, independent. It may be self-selecting. It may strike down decisions of the Executive or the Legislature. On the other hand, it may have a capacious doctrine of political question such that many such decisions are not justiciable.

4) there is an Army and a professional Civil and Diplomatic Service. It may have countervailing power.

5) there may be corporate interests- e.g. Trade Unions, Professional Associations, Business lobbies etc- which too have countervailing power.

It is also possible that a country may have plebiscites or referendums on particular issues. Here the majority of voters get to directly decide particular matters of policy.

What has never happened and can never happen is a mechanism whereby individual preferences over all social states are aggregated so as to give rise to a Social Choice function. The thing is not mathematically feasible because of problems of complexity, concurrency, computability and categoricity. Moreover, preferences are epistemic and impredicative and thus have no well defined mathematical expression.

Sadly, over the last 75 years, some stupid Mathematical Economists have ignored this obvious truth and written nonsense about a mathematical impossibility.

The Stanford Encyclopaedia of Philosophy's article on Social Choice Theory gives us a flavour of the Alice in Wonderland world which Social Choice theorists live in.

    Social choice theory is the study of collective decision procedures and mechanisms.

    This is what political analysts do. It is an ideographic matter. Forecasters try to figure out what issue most matters to particular types of voters and thus they try to predict the outcome of elections or else they advise candidates on 'messaging'- i.e. what to emphasize when appealing for votes.  

    It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs (e.g., votes, preferences, judgments, welfare) into collective outputs (e.g., collective decisions, preferences, judgments, welfare).

    Political analysts do look at votes and preferences. They conduct opinion polls and compare the actual behaviour of voters with what what they said they would do or what they said was important to them. Sometimes, it is the personality of the candidate which garners votes, not the policies they advocate. At other times, the reverse is the case.  

    Central questions are: How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options?

    The answer is that they form expectations on the basis of available information or, more commonly, on the bases of their own prejudices and cognitive biases. 

    What are the properties of different voting systems?

    This is a matter for political scientists or commentators.  

    When is a voting system democratic?

    When it gives us the outcome we want. Otherwise it is nothing but Fascism.  

    How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members’ individual preferences or judgments?

    It can say it spent some time trying to do this by canvassing opinions and consulting with interested parties. However, the outcome is arbitrary because at some point, the trigger must be pulled.  

    How can we rank different social alternatives in an order of social welfare?

    We can do so arbitrarily and then seek to justify our ranking.  

    Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems.

    Sadly, what they are doing is eating their own shit. 

    Pioneered in the 18th century by Nicolas de Condorcet and Jean-Charles de Borda and in the 19th century by Charles Dodgson (also known as Lewis Carroll), social choice theory took off in the 20th century with the works of Kenneth Arrow, Amartya Sen, and Duncan Black.

    None of whom were ever consulted by actual politicians. If their theories weren't utterly stupid, they would have had predictive power and thus they would have been much sought after by political parties.  

    Its influence extends across economics, political science, philosophy, mathematics, and recently computer science and biology.

    It has been a waste of time wherever it has been taken up. The thing is nothing but a cascade of intensional fallacies.  

    Apart from contributing to our understanding of collective decision procedures, social choice theory has applications in the areas of institutional design, welfare economics, and social epistemology

    But those 'applications' were mischievous or useless. 

    The law of large numbers states that as the size of the sample increases the sample mean converges to the true mean. Restated, this is the Condorcet Jury theorem. But it is not something peculiar to Social choice. Indeed, in a given society it is likely that some agents know more than other agents and a better choice is made if only the knowledgeable agents are consulted. Thus the Judge decides matter of law- of which he has expertise- but the jury decides such matters of fact where they are equally competent. However, the Judge may stipulate that they must heed the testimony of a particular expert witness, while disregarding that of another witness who, it is likely, has been bribed to give a particular testimony. 

    Condorcet’s second insight, often called Condorcet’s paradox, is the observation that majority preferences can be ‘irrational’ (specifically, intransitive) even when individual preferences are ‘rational’ (specifically, transitive).

    If such is the case, a representative or other body with authority can recognize this fact. They may use some arbitrary method to break the tie or otherwise prevent cyclicity.  Alternatively, there may be some 'horse trading' or bribery. In econ, this is called 'transferable utility'- i.e. money changing hands. What is important to note is that preferences may be 'strategic'- i.e. people deliberately create a tie in the hope of a pay off. 

    It is foolish to give a mathematical treatment to a situation where 'preference revelation' is a fundamental problem- i.e. where there is no 'Momus window' into the soul such that we can establish what a person's true motivations are. Still, for the purpose of pragmatic mechanism design, we can assume a 'Revelation Principle' such that for a large enough sample, people have no incentive to act strategically. 

    Arrow introduced a general approach to the study of preference aggregation,

    sadly, since preferences are epistemic and impredicative there is no well defined 'extension' (set) corresponding the intension 'Preferences'. Thus no mathematical or logical work can be done in this area. There are no sets and no functions. Still, for some rough and ready purpose we can arbitrarily assume the thing exists so as to make a prediction. But, that's what political analysts, not economists, do.  

    partly inspired by his teacher of logic, Alfred Tarski (1901–1983), from whom he had learnt relation theory as an undergraduate at the City College of New York (Suppes 2005).

    A relation denotes some kind of relationship between two objects in a set. Sadly, if there is 'impredicativity'- e.g. one object depends on the value of another object which in turn depends on its value (which is often the case for epistemic objects) - then there is no set.  The thing is not 'well defined'. Arbitrarily, for some purpose we can assume they are independent but though that may be useful, it is not mathematically sound. 

    Arrow considered a class of possible aggregation methods, which he called social welfare functions,

    If there is a function then there must be a graph of the function. But with epistemic objects there is no such graph because of impredicativity. This is nonsense piled on nonsense.  

    and asked which of them satisfy certain axioms or desiderata.

    The answer is obvious. Social Choice is delegated to some authoritative body. It may be elected or it may be (like the Judiciary) staffed by people with expertise in a particular field. There is no 'pure democracy' under the Sun. I suppose some small city state thousands of years ago could have periodic meetings of the entire adult population but the result- as the example of ancient Athens teaches us- was seldom good. Such states were absorbed by big Empires staffed by 'logothete' bureaucrats or Military pro-consuls.  

    He proved that, surprisingly, there exists no method for aggregating the preferences of two or more individuals over three or more alternatives into collective preferences,

    there is also no method of aggregating the preferences of one individual over one alternative- e.g. whether to fart. Sometimes you fart when you don't want to and sometimes you can't fart though the situation calls for nothing less.  

    where this method satisfies five seemingly plausible axioms, discussed below.

    Those 'axioms' were crazy shit.

    William Riker (1920–1993), who inspired the Rochester school in political science, interpreted it as a mathematical proof of the impossibility of populist democracy (e.g., Riker 1982).

    Yet populist democracies exist. The fact that their behaviour violates 'transitivity'- e.g. guys who voted against Trump four years ago decided to vote for him this time- is explained by the fact that everybody violates it all the time.  

    Others, most prominently Amartya Sen (born 1933), who won the 1998 Nobel Memorial Prize, took it to show that ordinal preferences are insufficient for making satisfactory social choices and that social decisions require a richer informational basis.

    Which isn't available. People act strategically- i.e. they tell lies. There is no 'Momus window' into the soul.  

    Commentators also questioned whether Arrow’s desiderata on an aggregation method are as innocuous as claimed or whether they should be relaxed

    They were nonsense. Why was this not obvious? The answer is that mathsy guys can be as stupid as fuck. Arrow's theorem looks like magic. That is because it is nonsense. 

     The lessons from Arrow’s theorem depend,

    on not understanding that epistemic objects- e.g. Preferences- are impredicative and have no well defined extension. There are no sets or functions in this realm. Social Choice theory is just an availability cascade of 'masked man fallacies' first described in the fourth century BC.  

    in part, on how we interpret an Arrovian social welfare function. The use of ordinal preferences as the ‘aggreganda’ may be easier to justify if we interpret the aggregation rule as a voting method than if we interpret it as a social evaluation method.

    This is mere semantics. You vote based on your evaluation. However, you may do so strategically- e.g. voting for Trump to punish Kamala for not supporting the Palestinians though you know that Trump doesn't give a fart for them.  

    Sen argued that when a social planner seeks to rank different social alternatives in an order of social desirability (thereby employing some aggregation rule as a social evaluation method), it may be justifiable and even necessary to use additional information over and above ordinal preferences, such as interpersonally comparable welfare measurements (e.g., Sen 1982) or information about people’s capabilities to achieve valuable functionings (e.g., Sen 1992).

    Sen is Bengali. There is a strong Fascist streak in the Bengali. They want a strong leader who does whatever he wants. Alternatively, maybe the Bench could usurp all power and do whatever stupid shit Bengali economists want to see done.  

    Arrow himself held the view

    ‘that interpersonal comparison of utilities has no meaning

    Because a guy who says 'I really really want to fuck my best friend's wife. I would get more utility from fucking her than he would' is making an interpersonal comparison of utility. Sen did in fact run off with his best friend's wife. Arrow didn't want the same thing happening to him.  

    and … that there is no meaning relevant to welfare comparisons in the measurability of individual utility.’ (1951/1963: 9)

    You can always give such a meaning to 'preference intensity'. Sen was prepared to wreck his career in India by running off with his best friend's wife. Fortunately, he landed on his feet at the LSE. Still, there was a time when other Bengali economists made fun of him because he had to iron his own shirts and didn't even have a chauffeur. Then he married a Rothschild.  

    Nowadays most social choice theorists have moved beyond the negative interpretations of Arrow’s theorem and are interested in the trade-offs involved in finding satisfactory decision procedures and the possibilities opened up by relaxing certain restrictive assumptions.

    This is cool if you are a UN bureaucrat or enjoy attending Conferences where everybody can virtue signal while claiming fat per diems.  

    Sen has promoted this ‘possibilist’ interpretation of social choice theory (e.g., in his 1998 Nobel lecture).

    In other words, wasting money for high minded reasons. Consider the plight of starving people. Many of them may not know that eating nice food will be beneficial to them. Moreover, some of them may be Lesbian. Just sending food to these starving people would be a grave injustice. We must consider the Capabilities and Functionings of starving Lesbians. Consider their ability to jump up and down. Just giving them food may distract them from developing this valuable functioning or Capability.  

    Moreover, as Fabienne Peter has argued, by moving beyond the narrow informational basis leading to the classic impossibility results, social choice theory can become a more promising framework for policy evaluation and offer resources for taking into account the situated nature of people’s agency, inequalities between them, and issues of gender (Peter 2003).

    In other words, you can virtue signal like crazy while criticizing the FAO and the Gates Foundation for wanting to 'help' starving Lesbians by giving them food and medicines while completely neglecting their 'agency' and capability to jump up and down.  

    In contemporary social choice theory, it is perhaps fair to say, Arrow’s axiomatic method is more influential than his impossibility theorem itself (on the axiomatic method, see Thomson 2000).

    Arrow neglected Knightian Uncertainty. That's why Arrow Debreu securities are 'weapons of mass financial destruction'. As for Social Choice theory, it is neither concerned with Society nor with Choice. It is merely pseudo-mathsy masturbation.  

    The paradigmatic kind of result in formal work is now the ‘characterization theorem’.

    In mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it. The problem here is that epistemic objects have no mathematical characterization. They can't be logically equivalent to anything, even themselves, because Leibniz's laws have no purchase on them.

    Here the aim is to identify a set of plausible

    plausible to fucking morons 

    necessary and sufficient conditions that uniquely characterize a particular solution (or class of solutions) to a given type of collective decision problem.

    One can give an arbitrary extension to relevant intensions for some particular purpose. But there are no necessary of sufficient conditions for what is merely arbitrary. Either the thing is useful enough or it can't 'pay for itself' and must be discarded. 

     Two points about the concept of an aggregation rule are worth noting. First, under the standard definition, an aggregation rule is defined extensionally, not intensionally:

    the problem is that epistemic objects don't have well defined extensions. You can arbitrarily assign such an extension for some practical purpose and this may be useful in a rough and ready fashion. But as our knowledge base changes, that 'extension' becomes less and less useful. Back in 2007, it seemed obvious to me that a black man named Barak Hussein Obama was unelectable. In 2015, it seemed obvious that a fat pussy-grabbing Billionaire was unelected. Women would vote overwhelmingly for Hilary as would African Americans and Hispanics. I was wrong.  

    it is a mapping (functional relationship) between individual inputs and collective outputs, not a set of explicit instructions (a rule in the ordinary-language sense).

    Sadly, it isn't a mapping because there is no well defined 'graph of the function'. We can pretend otherwise for some practical purpose, but this is pretence. It isn't mathematics.  

    Different sets of instructions could in principle give rise to the same mapping from inputs to outputs. Secondly, an aggregation rule is defined for a fixed set of individuals N and a fixed decision problem, so that majority rule in a group of two individuals is a different mathematical object from majority rule in a group of three.

    There is no 'mathematical object'. There may be an arbitrary mathematical assignation for some particular purpose. 

    One potential disadvantage of this way of defining an aggregation rule is that it makes it harder to determine how a given aggregation rule is to be extended to inputs outside the function’s formal domain.

    Or inside it. Our preferences are epistemic and impredicative. Moreover, there is regret minimizing behaviour which militates for 'discovery' and 'FOMO' (fear of missing out). We don't have a model for individual choice much less preference formation where there are 'Tardean' effects and other sorts of 'crowd psychological' effects.  

    By contrast, if we were given an explicit set of instructions, it might be easier to infer, for instance, how these are to be extended from the case of +1

    The principle of induction falls down in the one person, one alternative, case. Should I have a decision rule or not? No. It is a waste of time. Suppose someone else joins me. Should we have a decision rule? No. It is silly. A third person arrives. Now there is a 'tie breaker'. Should we have a decision rule? No. The other two may gang up on me. The result is we have no decision rule for all social states. We may cobble together some mechanism for specific 'collective action problems'. But there will be 'transferable utility' more particularly to solve 'hold out' problems. With bigger numbers, you may have elections to decide fiscal questions (Taxation can rise if you have Representation), but you would also have 'Checks and Balances' and a pretty opaque sort of politics conducted in smoke filled rooms. There will be 'log rolling' and 'pork barrel' politics and a continuous attempt to make the policy space more and more multi-dimensional so that, by the McKelvey chaos theorem, 'agenda control' becomes more and more important. In other words, you would get the pig's breakfast we see in democratic countries around the world today. Still, the alternative would be worse. King Trump would be worse than President Trump. 

    One other point. Social alternatives are infinite. Consider a single period economy where my alternatives are 'fart' or 'don't fart'. I can add the alternative 'fart if Mochizuki's proof of the abc theorem is valid' or 'Don't fart if Jennifer Aniston is a fat Australian man' and so forth. In practice, voting is seldom just about the candidates. You may vote to register a protest against things in general or abstain from voting because you think things in general are perfectly fine. My own concern is that Jennifer Aniston may actually be a fat Australian man. Australians are very good actors. What if I have been beating my meat while imagining an Ozzie dude? OMG! What if I'm Gay! 

    May (1952)  introduced four requirements:

    Universal domain: The domain of admissible inputs of the aggregation rule consists of all logically possible profiles of votes v1,v2,,vn, where each vi{1,1}.

    Presumably voting is compulsory. Even so, these 'profiles' are post hoc. We may assume they correspond to 'preferences' but can't be sure. 

    Anonymity: For any admissible profiles v1,v2,,vn and w1,w2,,wn that are permutations of each other (i.e., one can be obtained from the other by reordering the entries), the social decision is the same, i.e., f(v1,v2,,vn)=f(w1,w2,,wn).

    So, this does not apply to a representative democracy where voters in 'swing states' may have more influence on the outcome. Also, though elections may change who the legislators are, it may not change the social decision. Finally, 'anonymity' scarcely exists where people 'vote their caste' rather than just cast their vote.  

    Neutrality: For any admissible profile v1,v2,,vn, if the votes for the two alternatives are reversed, the social decision is reversed too, i.e., f(v1,v2,,vn)=f(v1,v2,,vn).

    Elections have magical properties. Thus when FDR was elected as the man who kept and would keep the US out of the war, the US stayed out of the War. 

    Positive responsiveness: For any admissible profile v1,v2,,vn, if some voters change their votes in favour of one alternative (say the first) and all other votes remain the same, the social decision does not change in the opposite direction;

    That's why the US did not enter the Second World War. Tojo and Hilter won.  

    if the social decision was a tie prior to the change, the tie is broken in the direction of the change, i.e., if [wi>vi for some i and wj=vj for all other j] and f(v1,v2,,vn)=0 or 1, then f(w1,w2,,wn)=1.

    Sadly, the direction of the change may be opposite to that which was voted for.  

    Universal domain requires the aggregation rule to cope with any level of ‘pluralism’ in its inputs;

    Suppose we vote for a guy thinking he will do x. He then does the opposite perhaps because of exogenous pressure. We may still rebel and kill him. Elections don't have magic powers.  

    anonymity requires it to treat all voters equally;

    Though some voters have more power to select candidates or set the agenda 

    neutrality requires it to treat all alternatives equally; and positive responsiveness requires the social decision to be a positive function of the way people vote. May proved the following:

    Theorem (May 1952): An aggregation rule satisfies universal domain, anonymity, neutrality, and positive responsiveness if and only if it is majority rule.

    Sadly, 'majority rule' may involve the collapse of the state. Aggregation rules have no magical powers. If a country does stupid shit, it may cease to be a country. That is why successful Democracies have 'checks and balances'. In any case, what voters may really want is that sensible things are done. They may not want 'majority rule' because this would mean the collapse of the country. 

    Apart from providing an argument for majority rule based on four plausible procedural desiderata,

    there is no 'argument' here. May merely described the way he thought universal suffrage works. He was wrong.  

    the theorem helps us characterize other aggregation rules in terms of which desiderata they violate.

    No. It is obviously shite.  

    Dictatorships

    May be wildly popular.  

    and weighted majority rules with unequal individual weights

    e.g. the system the US and the UK have 

    violate anonymity.

    people who live in 'swing states' or constituencies know that they will be courted by all political parties. They will seek to translate this into economic benefits.  

    Asymmetrical supermajority rules (under which a supermajority of the votes, such as two thirds or three quarters, is required for a decision in favour of one of the alternatives, while the other alternative is the default choice) violate neutrality.

    But may be necessary to prevent the country going up in flames.  

    This may sometimes be justifiable,

    Anything at all may be justifiable under some circumstance. Most countries have a 'State of Exception' whereby the Executive can wield emergency powers.  

    for instance when there is a presumption in favour of one alternative, such as a presumption of innocence in a jury decision.

    I suppose one might say that the doctrine of political question presumes the Executive acts in the public interest. 

    Symmetrical supermajority rules (under which neither alternative is chosen unless it is supported by a sufficiently large supermajority) violate positive responsiveness.

    So does the fact that wishes aren't horses which beggars are welcome to ride.  

    Some societies can only survive with 'majority rule'. But this may be done democratically or dictatorially or by some other traditional type of social mechanism. Other societies can't survive with 'majority rule'. The experiment of democracy is soon given up and you have the rule of a strong-man though this may be disguised by fraudulent elections. 

    In practice, 'preference intensity' can express itself in various ways- e.g. by raising funds for lobbying or political activism or else by establishing a 'threat point' such that the Executive fears a confrontation with a particular interest group. 

    Economists may not be aware that all Societies have some sort of legal system which holds certain activities to be repugnant. Legislatures may be able to change this but may lack the incentive to do so. Sometimes the Courts step in to move matters along or else the letter of the law ceases to be enforced. 

    Although the weak Pareto principle is arguably one of the least contentious ones of Arrow’s conditions,

    it is meaningless. Nobody knows if it applies. Some will falsely claim they are adversely affected and demand compensation. Others may fear the thing is 'the thin end of the wedge' or invoke 'Chesterton's fence'- i.e. the notion that there must be a good thing our ancestors didn't permit the thing. 

    Sen (1970a) offered a critique of it that applies when the aggregation rule is interpreted not as a voting method, but as a social evaluation method

    it is not a method. We merely say 'if people voted for this, they must want it and consider it superior to what went before.'  

    which a social planner can use to rank social alternatives in an order of social desirability. Here, the alternatives are understood not as coarse-grained electoral options but as more richly specified states of society.

    Sadly, only a dude who knows a lot about a particular society can make this specification. Mathematical economists don't know shit about shit.  

    Sen showed that, in this setting, the Pareto principle conflicts with a ‘liberal’ principle, which—he suggested—a social planner ought to respect.

    It doesn't. This is because nobody knows what it requires. 

    The liberal principle requires that each individual be given some basic rights, to the effect that his or her preferences are sometimes socially decisive (i.e., cannot be overridden by others’ preferences).

    No. Liberalism upholds the rule of law such that people have defeasible Hohfeldian immunities in certain matters.  

    Intuitively, each individual has a personal sphere in which this individual alone should be able to decide what happens.

    This is not the case. All Hohfeldian incidents are defeasible. In other words, under certain circumstances a particular immunity is cancelled by some superior entitlement enjoyed by some other party.  

    To give a trivial example, I alone should be able to decide whether I sleep on my right side or on my left side, and the same should be true for everyone else.

    No. There may be some sick person who must only sleep on his right side and this rule may be enforced by the hospital staff.  Suppose he finds this unreasonable and approaches the court. The judge may rule that he is not competent to decide what is best for himself. It permits the hospital staff to continue to restrain him from sleeping on his left side. 

    So, if two social alternatives, xx and yy, differ only with respect to the side on which individual ii sleeps, then individual ii’s preference between xx and yy should determine the social preference between xx and yy.

    We don't know how any two social alternatives differ. A court may accept expert testimony. But that testimony may be wrong.  

    (Recall that alternatives are here understood as richly specified states of society.)

    Which are unknown and unknowable to us.  

    Sen’s ‘minimal liberal’ requirement says that at least two individuals in society should have such a decisiveness right between two alternatives each.

    There is no such requirement in any liberal society under the rule of law. All Hohfeldian incidents are defeasible.  

    To illustrate the conflict between minimal liberalism and the weak Pareto principle, Sen asked us to imagine a society that consists of two individuals, Lewd and Prude, faced with the decision of who among them (if any) should read a controversial book, Lady Chatterley’s Lover.

    This is a question about 'repugnancy' markets. At one time, material which might cause people to masturbate was considered repugnant. This was because masturbation was considered very harmful. We no longer think that way.  

    In Sen’s story, Lewd most prefers that Prude read the book (alternative x)x),

    just as Prude most prefers that Lewd enter a Convent and take Holy Orders. It isn't an actual preference. It is like my saying 'I wish pigs could fly. I bet that would fly over Trump's head and shit on him'.  

    second-most prefers that he (Lewd) read the book himself (alternative y)y), and least prefers that neither of the two read the book (z)(z). Prude most prefers that neither read the book (z)(z), second-most prefers that he (Prude) read the book himself (x)(x), and least prefers that Lewd read the book (y)(y). Assuming Lewd is decisive over the pair yy and zz, society should prefer yy to zz.

    This is nonsense. The matter is justiciable. The Court may ban the book if approached by Prude. It may reverse the ban if Lewd assembles experts to testify to the book's literary value. Neither Prude no Lewd are decisive. The Court is.  

    Sen generalized this problem—now known as the ‘liberal paradox’—as follows.

    Theorem (Sen 1970a): There exists no preference aggregation rule satisfying universal domain, acyclicity of social preferences, the weak Pareto principle, and minimal liberalism.

    We don't and can't know that because there may, after our species has died out, be a way of 'factorizing' everything in our social or psychological sphere such that all epistemic 'intension's have well defined 'extensions' (in other words, nothing would be impredicative because we have found independent elements for all epistemic sets. At that point, there may be a non-arbitrary aggregation rule. But it would not be known to us. It would be known to some advanced species which has the technology to uncover all relevant facts about our species. 

    This result suggests that if we wish to respect individual rights, we may sometimes have to sacrifice Paretian efficiency.

    Nobody knows what is or isn't a Pareto improvement. The thing is epistemic and changes as our knowledge base changes.  

    Hence, Sen’s spoke of the ‘impossibility of a Paretian liberal’.

    Though plenty of such people existed and were personally known to Sen. I suppose, as a Bengali, he preferred Fascism or Communism to Liberal Democracy though he had to pretend otherwise so as to get the Nobel Prize.  

    An alternative conclusion is that the weak Pareto principle can be rendered compatible with minimal liberalism only if the domain of admissible preference profiles is suitably restricted, for instance to preferences that are ‘tolerant’ or not ‘meddlesome’ (Blau 1975; Craven 1982; Gigliotti 1986; Sen 1983).

    In which case Liberalism would be banned. It is rather intolerant of intolerant despots.  

    Lewd’s and Prude’s preferences in Sen’s example are ‘meddlesome’.

    No they differ as to what is or isn't a repugnancy market. There is an issue of public policy at the bottom if their disagreement. Sen invented a fantastic detail, viz Lewd wants Prude to read the book while fisting herself vigorously, in order to pretend that there is some 'meddlesome' aspect to their preferences.  

    Each of them ‘meddles’ with the other’s private sphere.

    No. It is obvious that when I say 'I wish you'd grown a pair of titties and spend all your time playing with them', that I am not expressing a preference relevant for Social Choice.  


    However, several authors have challenged the relevance of Sen’s result, by arguing that his ‘minimal liberalism’ condition uses an inadequate formalization of the notion of individual rights (e.g., Gaertner, Pattanaik, and Suzumura 1992; Dowding and van Hees 2003).

    Those nutters don't understand that 'rights' are merely a bundle of defeasible Hohfeldian incidents. What matters if there is an obligation holder for whom providing remedies is incentive compatible. 

    The Gibbard Satterthwaite theorem, anticipated by Dummett & Farquharson, merely states what everybody has always known, everything political involves lying- i.e. 'strategic behaviour'. 

    Universal domain: The domain of ff is the set of all logically possible profiles of complete and transitive individual preference orderings.

    It is unknowable which is why it can't be a domain or range or set of any type.  

    Non-dictatorship: There does not exist an individual i∈Ni∈N such that, for all ⟨R1,R2,…,Rn⟩⟨R1,R2,…,Rn⟩ in the domain of ff and all xx in the range of ff, yRixyRix where y∈f(R1,R2,…,Rn)y∈f(R1,R2,…,Rn).[7]

    Nothing wrong with their being a dude who always happens to vote the right way. A Dictator is a guy who can kill his rivals. The question is whether it is known that such an individual exists. If so, his saying he will vote a particular way may alter outcomes. He functions like an Oracle or the millionaire in Newcombe's problem.  

    The range constraint: The range of ff contains at least three distinct alternatives (and ideally all alternatives in X)X).

    We don't know if they are distinct. We vote for Smith rather than Jones or Brown but later realize that Smith will do exactly what Brown would have done. As for Brown, he was only put up to split the vote for Jones. 

    When supplemented with an appropriate tie-breaking criterion, the plurality and Borda rules can further be made ‘resolute’:

    Resoluteness: The social choice rule ff always produces a unique winning alternative (a singleton choice set). 

    Why should it? If voting uncovers new information, maybe it would be better to run the thing again. Moreover, we don't know if unicity obtains. Any political outcome may in fact be multiply realizable.  

    Surprisingly, this list of conditions conflicts with the following further requirement.

    Every linguistic or social practice conflicts with it. People tell lies. Sad.  

    Strategy-proofness: There does not exist a profile ⟨R1,R2,…,Rn⟩⟨R1,R2,…,Rn⟩ in the domain of ff at which ff is manipulable by some individual i∈Ni∈N, where manipulability means the following: if ii submits a false preference ordering R′iRi′ (≠Ri)(≠Ri), the winner is an alternative y′y′ that ii strictly prefers (according to Ri)Ri) to the alternative yy that would win if ii submitted the true preference ordering RiRi.[8]

    Anybody can be fooled by anybody or may be unable to do anything about the other's blatant lies.  

    Theorem (Gibbard 1973; Satterthwaite 1975): There exists no social choice rule satisfying universal domain, non-dictatorship, the range constraint, resoluteness, and strategy-proofness.

    Sadly, this can't be proved mathematically because we have no access to well defined sets. The problem with the 'intensional fallacy' is that nothing whatsoever can be said about epistemic objects. They change as the knowledge base changes or as bigotry spreads. 

    I suppose Gibbard Satterthwaite was useful because it changed the focus to 'mechanism design' and incomplete contract theory. But, at the end of the day this is ideographic and has always been done by those with relevant skill and expertise even if they don't talk about it honestly. What was comic was that the post Gibbard literature mentioned computational problems. But such problems also kills off Arrow-Debreu. The time class for the solution to General Equilibrium is exponential. The Capabilities approach is founded in Arrow-Debreu. Thus, it it too is ab ovo useless. 

    Welfare Economics is part and parcel of the theory of Public Finance. If money raised by taxation is used to solve collective action problems, Income rises and thus Tax revenue rises. There is a virtuous circle. A.O Hume, setting up the Indian National Congress, tried to explain this to Indians. Sadly, they were only interested in virtue signalling and pretending the Viceroy had a magical money tree and was refusing to use it to buy starving Indians some nice food to eat. Consider 

    Sen’s extension of Arrow’s framework

    An assumption built into Arrow’s framework is that preferences are ordinal and not interpersonally comparable:

    in any objective sense. But I can look around and find someone doing better than me and try to imitate him.  

    preference orderings contain no information about each individual’s strength of preference or about how to compare different individuals’ preferences with one another.

    You could look at how much people will pay or how many buses they will burn down to get what they want. That's a measure of preference intensity.  

    Statements such as ‘Individual 1 prefers alternative xx more than Individual 2 prefers alternative yy’

    us if the second dude give up yy so that the first gets xx. Money may change hands to facilitate this.  

    or ‘Individual l prefers a switch from xx to yy more than Individual 2 prefers a switch from x∗x∗ to y∗y∗’ are considered meaningless.

    Arrow-Debreu was meaningless. In any case, it was 'anything goes'.  

    In voting contexts, this assumption may be plausible, as we often may not be able to elicit more information from voters than their ordinal rankings of the options.

    Fuck off! Pollsters spend a lot of money getting such information.  

    But in welfare-evaluation contexts—when a social planner seeks to rank different social alternatives in an order of social welfare—

    there has never been any such Benthamite planner. There may be a bit of money for 'project appraisal' or 'Cost Benefit analysis' but this was just window dressing. He who paid the piper called the tune. He might also pay for some dude to say it was a very nice tune. Sen and his best friend wrote a paper hinting at this before Sen ran off with his best friend's wife to London.

    the use of richer information may be justified.

    Bureaucrats and 'activists' are welcome to gas on about this. But nothing gets done unless some oligarch pays the fucking piper and goes ahead with the project. 

    Sen (1970b) generalized Arrow’s framework to incorporate such richer information.

    As before, consider a set N={1,2,…,n}N={1,2,…,n} of individuals (n≥2)(n≥2) and a set X={x,y,z,…}X={x,y,z,…} of social alternatives.

    Those alternatives are unknown.  

    Now each individual i∈Ni∈N has a welfare function WiWi over these alternatives, which assigns a real number Wi(x)Wi(x) to each alternative x∈Xx∈X, interpreted as a measure of ii’s welfare under alternative xx.

    Sen noticed that starving Indian villagers where too busy assigning such numbers to grow food to eat.  

    Any welfare function on XX induces an ordering on XX, but the converse is not true: welfare functions encode more information.

    They don't exist. Unicorns encode a lot of information. If they shove their horn up your bum you will become very enlightened.  

    A combination of welfare functions across the individuals, ⟨W1,W2,…,Wn⟩⟨W1,W2,…,Wn⟩, is called a profile.

    A social welfare functional (SWFL), also denoted FF, is a function that assigns to each profile ⟨W1,W2,…,Wn⟩⟨W1,W2,…,Wn⟩ (in some domain of admissible profiles) a social preference relation R=F(W1,W2,…,Wn)R=F(W1,W2,…,Wn) on XX, with the familiar interpretation. Again, when FF is clear from the context, we write RR for the social preference relation corresponding to ⟨W1,W2,…,Wn⟩⟨W1,W2,…,Wn⟩. The output of a SWFL is similar to that of a preference aggregation rule (again, we do not build the completeness or transitivity of RR into the definition[9]), but its input is richer.

    There is a feasible social state which we would all prefer. It is one where there is virtually free energy and everybody has a  3-D printers which make us anything we want. Sadly, our Scientists haven't yet discovered how to build such things. I suppose they will at some point in the future. The problem with Sen-tentious shite is that it pretends there are no epistemic problems. We already have all possible knowledge.  

    What we gain from this

    is nothing. It is a fairy story.  

    depends on how much of the enriched informational input

    which is wholly inaccessible to us 

    we allow ourselves to use in determining society’s preferences:

    Society told Social Choice theorists to fuck the fuck off. That was their preference. Sen had and has no power. Manmohan was a two term PM. Even Yunus is now running Sen's ancestral East Bengal. Stuff like Trade theory or Micro-credit is real. Social Choice theory is shitting higher than your arsehole.  

    technically, it depends on our assumption about measurability and interpersonal comparability of welfare.

    Just as gaining enlightenment when a unicorn shoves its horn up our rectum depends on our assuming such unicorns exist. 

    By assigning real numbers to alternatives,

    magical powers are gained. 

    welfare profiles contain a lot of information

    Sadly, if I assign you the number 2476563 no information is gained. 

    over and above the profiles of orderings on XX they induce.

    For example, it is discovered that not only are you inferior to me (because I am number one on this list of lovely peeps) but also you are odd. Why don't you just top yourself, you loser?  

    Many different assignments of numbers to alternatives can give rise to the same orderings.

    So the thing has no unicity. It is wholly arbitrary.  

    But we may not consider all this information meaningful. Some of it could be an artifact of the numerical representation. For example, the difference between the profile ⟨W1,W2,…,Wn⟩⟨W1,W2,…,Wn⟩ and its scaled-up version ⟨10⋅W1,10⋅W2,…,10⋅Wn⟩⟨10⋅W1,10⋅W2,…,10⋅Wn⟩, where everything is the same in proportional terms, could be like the difference between length measurements in centimeters and in inches. The two profiles might be seen as alternative representations of the exact same information, just on different scales.

    Also, if you multiply everything by 69, then fellatio and cunnilingus will increase exponentially.  

    To express different assumptions about which information is truly encoded by a profile of welfare functions and which information is not (and should thus be seen, at best, as an artifact of the numerical representation), it is helpful to introduce the notion of meaningful statements.

    No statement by Sen has been meaningful though all have been mischievous in some way.  

    Some examples of statements about individual welfare that are candidates for meaningful statements are the following 

    A level comparison: Individual i’s welfare under alternative xx is at least as great as individual jj’s welfare under alternative yy, formally Wi(x)≥Wj(y)Wi(x)≥Wj(y). (The comparison is intrapersonal if i=ji=j, and interpersonal if i≠ji≠j.)

    This is an arbitrary assertion. We don't know our own level of welfare. That's why we get a rude shock after visiting our Accountant or our Doctor. Still, if the horn of the omniscient unicorn simultaneously enters all our rectums, then Sen-tentious Social Choice theory might not be an utter wank. I omit the other comparisons mentioned in the article. The fact is such things have never existed because they are too costly and yield no benefit whatsoever. What can be done is estimating how much tax a factor will pay before it decides to fuck off. Public Finance matters. Welfare Econ does not. 

    Arrow’s view, as noted, is that only intrapersonal level comparisons are meaningful, while all other kinds of comparisons are not.

    They are highly meaningful. They drive mimetic effects and change Society. If you can spot such effects 'at the margin' you can make good predictions. You will be well paid and won't have to teach nonsense to credential craving imbeciles. 

    Still, it is worth pointing out that the Szpilrajn extension theorem shows that any ordinal ranking can give rise to a cardinal measure. So what? We neither have the one nor the other. The plain fact is utility either means 'money' or it is bullshit. Money talks. Bullshit walks. 

    I suppose a Dictator could hire a bunch of guys to do 'interpersonal comparisons' and calculate Cardinal Utility for everybody. They may show that what Jews really really want is to hand over all their property to Gestapo officers before hopping on a cattle truck to the gas chamber while whistling a merry tune. What would be pricelessly funny would be if some guy working for that dictator published a theorem showing that there could be a SWF which was non-dictatorial and fulfilled all Arrow's other conditions. 

    I suppose, Social Choice theory is inherently dictatorial because it assumes people won't tell it to fuck the fuck off. Rawlsian Social Contract theory is similarly flawed. No Contract is valid without the passing of consideration. Don't agree to anything unless you get paid.

    An important conclusion, therefore, is that Rawls’s difference principle, the classical utilitarian principle, and even the head-count method of poverty measurement can all be seen as solutions to Arrow’s aggregation problem

    just like the establishment of a Caliphate after the slaughter of all kaffirs, munafiqs and women who talk too loud.  

    that become possible once we go beyond Arrow’s framework of ordinal, interpersonally non-comparable preferences.

    Caliphate will go beyond Rawls and Sen. Did you know that what kaffirs really really want is to have their throats slit? True, some- like Sen's parents- may run away from East Bengal before this can happen but that is only because kaffirs are 'jahil'- i.e. ignorant. 

    I suppose Social Choice theorists and Moral Philosophers were beginning to realize that they had chosen a wholly useless profession. Smart people had gained money or wealth or great political influence. Moreover the working class had rebelled against 'equity' and 'redistribution'. They wanted higher living standards and admired self-made billionaires.

    ...minimal equity, requires (in the words of Sen 1977: 1548) ‘that a person who is going to be best off anyway does not always strictly have his way’,

    Unless people think he is smart and should have his way because society will benefit thereby. Meanwhile useless academics should be told to fuck the fuck off.  

    and another, separability, requires that two welfare profiles that coincide for some subset M⊆NM⊆N while everyone in N∖MN∖M is indifferent between all alternatives in XX lead to the same social ordering.

    Or not. Nobody cares because social orderings don't exist. I suppose Social Choice theorists- more particularly after mainstream Journals started to refuse to publish their shite towards the end of the Seventies- realized that they were pretty much at the bottom of the pecking order. Sen had to iron his own shirts in London while Manmohan lived in a mansion with lots of servants as head of the RBI. Then the fucker became Finance Minister and a great hero to India's middle class. Sen's cup of bitter waters overflowed.

    ‘prioritarian’ SWFLs sum up concavely transformed welfare, giving greater marginal weight to lower levels of welfare.

    like the lower welfare of Sen relative to Manmohan or the billionaire Purnendu Chatterjee. The Swedes gave this brown monkey a Nobel for having bravely resisted the temptation to starve to death. 

    What is the future of Social Choice theory? I think the answer is that it will converge to Ethology. It is likely that the true determinants of responses to collective action problems is a biologically deeper level than epistemic notions like 'preferences' and 'expectations'. Societies have to compete for scarce resources. Some will use 'costly signals' and gravitate to better 'separating equilibria' while others indulge in 'cheap talk' and lose control of resources. 

    Future historians might consider the vogue which Social Choice enjoyed between about 1950 and 1970 to have to do with the lingering memory of war-time planning and the belief that the Command Economies were catching up, or even surpassing, the Democracies. Equally, the rise of a mathematical Marxian theory seemed to require the RAND corporation and that portion of the Social Science establishment which required State funds to expand to come up with a 'mathsy' alterative. But it set its sights too low. It was merely saying, 'whatever a Command economy can do, we too can do by getting the incentive structure right'. What was missing was a Hayekian vision of the difficulties of information aggregation. Also, neglect of Knightian Uncertainty fatally vitiated the whole program. Then came the mathematical problems of computability, complexity, concurrency and the fact that category theoretical 'naturality' or unicity are far to seek. However, it was the 'intensional fallacy'- this business of pretending an epistemic object can be a set- which permitted this gawdy availability cascade to fascinate a generation of mathsy shitheads.  


    n
    +1 individuals and four alternatives.