Arrow's uselessness

 The following obituary from the Washington Post is a typical summary of Ken Arrow's contribution to Economics

In his 1954 paper with Gérard Debreu, Arrow proved the existence of equilibrium in a competitive economy.

This is nonsense. If there is no Knightian Uncertainty then there is no reason to have competition. There can be 'Aumann agreement' on 'public signals' for an optimal 'correlated equilibrium'. (In other words, the price vector is computable by everyone- in which case it is enough for it be done by one independent authority) There is also no reason to use language or, indeed, bother with education or scientific research. All information would already be reflected in the price vector. 

I suppose I should clarify that the two fundamental theorems of Welfare Econ & the folk theorem of repeated games merely say that a free market, or non coercive system, can achieve as good a result as a Command economy where 'shadow prices' are used to allocate resources. In other words, Arrow, Samuelson etc. are saying we can be as good as Kantorovich's USSR! Indeed, Samuelson kept saying the Soviets could overtake us in terms of material living standards even after Gorby had blown the whistle on GOSPLAN's inefficiency.

Of course, if the economy were non-dissipative and had a Noetherian and there genuinely were 'symmetries' and 'conserved properties'- whereas, actually, 'duality' in Econ, is arbitrary or wholly artificial- then, maybe, Arrow-Debreu shite would not be 'weapons of mass financial destruction' or programmatic, Sen-tentious, stupidity. 

One further point. Even if the concept of equilibrium is useful in the study of dissipative systems it is only because the concept of God as the sole efficient cause, or else an inaccessible 'slingshot' Truth, is useful rather than facile or fallacious. 

In doing so, he offered a rigorous foundation of Adam Smith’s conjecture: solely by pursuing their desires, the individual plans of consumer and producers are guaranteed to meet.

It is obvious that some of our desires can be satisfied by other people provided we satisfy some of their desires. There is still a coordination and concurrency problem of an epistemic, impredicative, type. Smith's advise was practical. Imitate what smarter, richer, peeps be doing. Stop drinking a lot of usquebaugh and sticking a dirk in your cousin. In politics, be as supercilious as the Sassenach, while, in business matters, be as down-to-earth as the Dutch. For fuck's sake don't succumb to I-talian Catholicism or whatever fucking craziness the Frogs are into. 

Now it is true that Smith wasn't utterly stupid and did have some vague idea of the Davenant-King result re. Income elasticity of Food and thus some inkling of a 'steady state' which, however, had been severely missing in North Europe for centuries- which is why darkies like me now spick Inglis. 

But this sort of 'steady state' has nothing to do with any type of general equilibrium though, no doubt, at the limit, arbitrage in certain areas could be said to transform a 'steady state' into a general equilibrium. But this is only because the same thing could be said to turn cats into dogs.  The plain fact is even if everybody's 'ex poste' and 'ex ante' is the same and even if everybody finds that when baby says 'buy me a bow wow', baby is perfectly happy to receive a kitten instead, even if all this is the case, there aint no fuckin' General Equilibrium. Why? It would be a 'pooling' one. Where have we seen any such thing? What we have are 'separating equilibria' based on costly signals, so that there is channelization of hedging and income effects- i.e. the stuff which renders General Equilibrium not just 'anything goes' but also impredicative, non computable, and (because of concurrency) wholly fucking arbitrary- not to mention the fact that every 'Tarskian primitive' in Arrow Debreu is epistemic and vitiated by the intensional fallacy. In other words this is useless nonsense which is also known to be shit for purely logical reasons. 

Still, I suppose one could say Arrow-Debreu is just Leibnizianism dressed up in shitty math (which violates Liebniz's law of Identity' because of the intensional fallacy). But, unlike Smith's  'invisible hand' which represents the 'mysterious economy' of the Katechon such that though we are all 'windowless monads' synchronized in pre-established harmony (though in Smith 'synderesis' or the 'impartial spectator' within our bosom plays a role), still we have the illusion of free will.  

While working at the RAND Corporation during the Cold War, Arrow’s supervisor wanted him to think about how to characterize the preferences of the Soviet Union.

Stalin's preferences were the preferences of the Soviet Union. This did involve killing lots of people or sending them to the Gulag. 

Anyway, RAND quickly discovered that what the Soviets- like the Brits, the French & even the Israelis- wanted was nukes and the means to deliver them by missile. Asking Arrow was a bad idea. he was as stupid as shit- i.e. an academic economist. It was like asking Chomsky to do something useful for the defence of his country. 

So Arrow started to think about the problem of how to translate individual preferences into a collective decision.

Since no algorithm can capture how individual preferences are transformed into individual decisions, it was obvious that the same would be true of collective decisions.  

Preferences are epistemic or 'impredicative'. Thus there is no 'extension' to the intension. There is no set or 'unique pre-order'. Thus the thing can't be described mathematically.

This led to his famous 1951 book, in which Arrow proved that there is no mechanism that can both satisfy a set of reasonable assumptions

they were crazy assumptions even assuming no Knightian Uncertainty. The 'non-dictatorship' assumption cashes out as if there is no dictator but it is possible that one guy might always happen to vote on the winning side, then that guy is actually a dictator!  

and translate the preferences of rational individuals into a coherent collective decision.

The set of decisions taken by entity X at time Y may not be 'compossible' though what actually happens- which may be stuff nobody wanted to happen-  has to be 'compossible' with our reality. Unless it doesn't. Maybe econ is actually about ontologically dysphoric goods and services. The relevant 'Lancastarian' characteristics space is not of this world. 

In other words, any mechanism of “preference aggregation”

which, because 'preference' has no well defined, non impredicative or epistemic, 'extension must be arbitrary or incomputable shite 

is either incoherent or dictatorial.

This is either a meaningless or a wholly arbitrary- indeed dictatorial!- assertion. Voters would immediately reject any Arrowvian mechanism. The thing is obviously stupid.  

By the same token, you can't prove any Social Choice mechanism whatsoever doesn't comply with any bunch of crazy, incompossible, restrictions. Why? The thing could be non-deterministic- i.e. 'verification' could be 'quick' but a computation could take longer than the life-time of the Universe.

If one is a bit shit at logic- as Arrow was- one can prove the existence of a Latin formula which, if uttered, causes the Devil to appear. But, what is lacking is 'verification'.

To put it concisely: in these two works, Arrow proved the existence of a solution to the problem of economics

provided there was no need for language or communication or cooperation of any type because everybody would wake up in the morning knowing exactly what they needed to do in return for which others would supply them with whatever they were entitled to without a word or a coin being exchanged.  

and the non-existence of a solution to the problem of politics.

Political problems are either solved or left to fester every day of the week. But that is also true of economic and scientific and marital and psychological and every other sort of problem. 

Arrow's work was meaningless though, like the religious doctrine of 'occasionalism', some may have found it useful for some private purpose.  

Arrow had three intellectual successors: Anthony Downs (a student of Arrow at Stanford),

whose work was just a restatement of Jevon's paradox just as Arrow's was a reworking of Condorcet. Still, 'mathematical politics' was less shitty than Continental shite.  

Mancur Lloyd Olson,

who invented the phrase 'stationary bandit'. 

and William Harrison Riker.

a founder of rational choice theory. 

Within political science, there have not been subsequent theories as innovative as those of Arrow, Downs, Olson and Riker.

But it is the Chinese Communist Party which has been the most successful political entity on the planet! Politicians who do stuff which helps the country get richer and stronger attract support. On the other hand, waging stupid, expensive, futile wars is probably a bad idea.

These remain the foundational building blocks of the discipline.

Which is as useless as is the theory of aesthetics if you want to become as beautiful and elegant as me.  

As argued in a recent book by Kevin Clarke and David Primo, science is essentially about models,

No. Science is about inventing cool or useful stuff. It uses models for that purpose. It isn't a fucking wank.  

and political science is no exception.

It is bullshit.  

It is precisely this set of models that informs our current understanding of politics.

But that understanding is shite.  

Olson defied the assumption that given a common interest individuals would form groups to pursue it.

There was no such assumption because if you are a horny dude you can't join an association for horny dudes. To do so would defeat the purpose. Horny dudes get laid precisely because women assume they are good enough at sex to have the thing offered to them on a plate. 

In doing so, he rendered collective action a puzzle to be explained, not something to be assumed.

Collective action, like individual action, can be shitty or self-defeating. This discourages spending time or money on either.  

Downs challenged the premise that political parties were agents of particular segments of society.

A parasite may well claim to be an agent. On the other hand, some parasites are actually symbiotes. That's why we drink probiotic yoghurt.  

Instead, he posited that they were the creatures of ambitious politicians seeking power.

This was always obvious.  

It was perhaps Riker who fully extracted the consequences of Arrow’s discovery. In “Liberalism Against Populism”, Riker contrasted these two strands of democratic theory.

which, ever since Reagan started speaking of the 'L-world', are as meaningless as accusing your rival of being totes Fascist.  

Derived from the writings of Rousseau,

a wanker who was literally insane- though he wrote well 

populism states that democratic choices — including election outcomes — are the reflection of a coherent collective will.

But any sort of will, coherent or otherwise, can be so wholly mischievous that people pay to suppress the thing.  

Consequently, an elected government carries a mandate to enact it.

No. It can justify certain actions by saying 'we have a mandate to do this' but the counterargument is 'no, you don't. The mandate was to do it only if circumstances were propitious.'  

Arrow’s theorem established that this conception is illusory.

But that theorem is nonsense. It is a case of ex falso quodlibet- from a stupid lie (e.g. a Dictator can exist secretly even if she has no authority or power of any sort) any stupid shit can be deduced.  

Electoral outcomes depend critically on electoral rules.

But if the rules are fucked, the outcomes can be pretty fucking horrible- think Lebanon.

Thus, they cannot be easily interpreted as mandates.

Anything can easily be interpreted as anything else.  

The most we can demand from democracy is the liberal, Madisonian version:

only if you live in a country where lots of lawyers and wannabe politicians know the difference between Madisonian Liberalism and Ashley Madison.  

a system of regular elections that provide opportunities to sanction governments that perform poorly.

Unless the alternative is obviously worse.  

Or, as the philosopher Karl Popper put it, citizens can rid of governments without bloodshed.

This can be done without democracy. Just keep telling the King, or Pope, or whatever that he smells bad and will have to clean our toilets if he wants us to give him a little money and the guy will take the hint and fuck off.  A government which is ignored and which can't raise taxes gets disintermediated. 

However pedestrian this conception of democratic government might look like, we can still can throw the rascals out.

You can always throw rascals out or just piss on their heads if that is more pleasurable. The point about representative democracy is that voters might be willing to pay taxes because they think their guys in Parliament will do sensible things with that money. 

Arrow teaches us that politics

like economics or marital relations 

has no “solution” — only ongoing conflict that is channeled through political institutions that lend at least some stability to the process.

The reverse is equally likely. Some polities become more stable after 'political institutions' are suppressed or rendered cosmetic.  

But the outcomes of this conflict are simply the contingent product of the struggle for power.

just as in economics or, indeed, the dynamics of families or clubs of various sorts. 

What we hope for is that politicians can devise strategies that produce compromises that, albeit temporary, can pave the way to civilized political life.

Like the Missouri Compromise- right?  

 The problem with Arrow is that he didn't get Knightian Uncertainty nor understand that the rational response to it is regret minimization. Instead, he thought there was something magical about Information. It ought to be perfect and ubiquitous even though, if such were the case, there would be no need for Society or any sociable type of relationship. 

The following passage is typical of Arrow-

When there is uncertainty, information or knowledge becomes a commodity.

We are absolutely certain that we will die. But information or knowledge about how to put off death is a commodity. But, for many people, so is investing in a better after-life. The thing is 'regret minimizing'.  

Like other commodities, it has a cost of production and a cost of transmission, and so it is naturally not spread out over the entire population but concentrated among those who can profit most from it.

No. Those who can most profit from it may offer a higher price to acquire it or to employ those who have it. But, it is equally likely, that they won't bother unless their rivals are doing so. 

(These costs may be measured in time or disutility as well as money.) But the demand for information is difficult to discuss in the rational terms usually employed.

Why? The fact is either information is valued in itself or else the demand for it is 'derived'. But this is true of any commodity. I buy a cake because I like cake. You buy a cake to take into work so as to gain the goodwill of your new colleagues. In the first case, I would be happy with the cake provided my circumstances had not changed. Thus, if I discover- as I have recently done- that I am diabetic, I am not happy when the cake I ordered is delivered. Equally, you may find that purchasing a cake was a bad decision. Your colleagues are fitness fanatics and now think of you as a big fat loser.  

The value of information is frequently not known in any meaningful sense to the buyer;

This is true of any speculative purchase or any 'discovery' process- i.e. trying a new restaurant serving a type of cuisine previously unknown to you.  

if, indeed, he knew enough to measure the value of information, he would know the information itself.

Nonsense! I know the value of information that will give my ageing PC a new lease of life. But I don't have that information. I seek a computer technician who can do what is required for a sum of money equal to or less than the value to me of a rejuvenated computer. 

But information, in the form of skilled care, is precisely what is being bought from most physicians, and, indeed, from most professionals.

No. I may have all the information needed to perform a surgical operation. But I don't have the necessary skill or, indeed, a medical license permitting me to perform surgery.  

The elusive character of information as a commodity suggests that it departs considerably from the usual marketability assumptions about commodities.

Information provision is a service. It may be complementary to some specific manual or mental skill which is difficult to acquire. Thus, I have the information that I suffer Type 2 Diabetes. But I need to see Nutritionists and Exercise Coaches as well as a host of other medical professionals so as to figure out a method of managing my condition.  

That risk and uncertainty are, in fact, significant elements in medical care hardly needs argument.

This is also true of automobile care or the sort of diligence a pedagogue should exercise. 

I will hold that virtually all the special features of this industry, in fact, stem from the prevalence of uncertainty.

Knightian uncertainty is ubiquitous. It exists in the market for pork bellies just as much as in that for petroleum or that for medical care.  

The nonexistence of markets for the bearing of some risks in the first instance reduces welfare for those who wish to transfer those risks to others for a certain price, as well as for those who would find it profitable to take on the risk at such prices.

How do we know those markets don't exist? It may be that there is an incomplete contract or other type of relationship such that this is what happens- at least implicitly and with the benefit of hindsight.  

But it also reduces the desire to render or consume services which have risky consequences; in technical language, these commodities are complementary to risk-bearing.

Incomplete contracts or good faith relationships can compensate for this.  Risk falls where there is 'survivability' or 'joint utility' such that 'catastrophic' risk is tamed 

Conversely, the production and consumption of commodities and services with little risk attached

we may think there is little risk attached. But the future may well be something we never imagined or anticipated. It turned out our 'safe' job was actually very risky.  

act as substitutes for risk-bearing and are encouraged by market failure there with respect to risk-bearing.

We don't know whether a market failure is a good or a bad thing till after the event. 

Thus the observed commodity pattern will be affected by the nonexistence of other markets.

Markets may be non-existent because relationships are superior in getting to the cooperative solution.  

' It should also be remarked that in the presence of uncertainty, indivisibilities that are sufficiently small to create little difficulty for the existence and viability of competitive equilibrium may nevertheless give rise to a considerable range of increasing returns because of the operation of the law of large numbers.

But this is also true if there is no fucking uncertainty- e.g. we can be pretty certain, as we eat our breakfast, that the world won't have greatly changed by lunch time. 

Since most objects of insurance (lives, fire hazards, etc.) have some element of indivisibility, insurance companies have to be above a certain size.

Everything has to be above a certain size in order to qualify as being a thing.  

But it is not clear that this effect is sufficiently great to create serious obstacles to the existence and viability of competitive equilibrium in practice.

There probably is a 'natural monopoly' for certain types of insurance- e.g. National Insurance- if the population is homogenous enough though there is likely to be a degree of cross-subsidization or price or service provision discrimination.  

One form of production of information is research.

Another is talking or listening or walking around with your eyes open.  

Not only does the product have unconventional aspects as a commodity,

some is certified as being marketable for a particular purpose. Some is a nuisance- e.g. dick pics sent to you by your g.f, as attachments to long missives informing you of your shortcomings in that department. 

but it is also subject to increasing returns in use,

No. There are diminishing returns to information. I gain by knowing the name of the medicine I should take for my diabetes. I don't really want to know more and more about its chemical composition. It is a different matter that more and more smart people will want this information. 

since new ideas, once developed, can be used over and over without being consumed,

Ideas are not consumed thought there is an opportunity cost to entertaining them. Ideas may be embodied in goods or services which can be purchased and which are 'rival' and 'excludable'.  

and to difficulties of market control, since the cost of reproduction is usually much less than that of production. Hence, it is not surprising that a free enterprise economy will tend to underinvest in research; see Nelson [211 and Arrow [4]

No. It may overinvest in some types of useless research and under-invest in stuff which can't give rise to intellectual property.