The poverty of Social Choice Theory

Less then ten years ago, Project Syndicate published the following- 

Social Choice and Social Welfare
Nov 26, 2014AMARTYA SEN

Human beings have always lived in groups, and their individual lives have invariably depended on group decisions.

No. Individual lives depend on individual decisions- including which group to live amongst and which group to run the fuck away from. Groups may not make any decisions whatsoever. Polities do make decisions- judicial, administrative, defense related, fiscal etc. But a Polity is not necessarily a collection of groups. It may be territorially defined and administered by one type of group while being defended by another group. Furthermore, groups may have a common resolve without having any collective decision making mechanism.

But, given the daunting challenges of group choice, owing to the divergent interests and concerns of the group’s members, how should collective decision-making be carried out?

The answer is that decision making should be delegated to those with ideographic, specialist, knowledge. At the least, those involved in collective decision making should have the opportunity to choose between the recommendations of experts.  

A dictator who wants to control every aspect of people’s lives will seek to ignore the preferences of everyone else.

No. A dictator will choose one strong preference and show herself to be better able to bring that situation about. Germans were actually anti-Semitic though German Jews were tremendously patriotic and productive. 

Dictators may use propaganda to artificially create  preferences but they would be foolish to ignore those that actually obtain.  This is because coercion is costly. The Dictator's Praetorian Guard or inner circle may be able to indulge themselves in various repugnant ways. But the pretense will be kept up that the opposite is the case. 

On the other hand, the Planning Commission- or some other bureaucratic body- may well ignore the preferences of everybody else. But, if the plan is not implemented there is no Dictator. There is only a waste of time. 

But that level of power is hard to achieve. More important, dictatorship of any kind can readily be seen to be a terrible way to govern a society.

No. A Dictatorship may be seen as the only way to govern a terrible society. But, equally, a Dictator may be appointed if that seems the best way to secure an important objective- e.g. National Defense, rapid Economic growth, securing the lives and property of minorities- etc.  

So, for both ethical and practical reasons, social scientists have long investigated how the concerns of a society’s members can be reflected in one way or another in its collective decisions, even if the society is not fully democratic.

No. There has been no such 'social science'. There is 'comparative politics' whereby existing polities are compared and ranked on how democratic they are. But, if the populations have different characteristics then there is little point to the exercise. The other point has to do with observer bias. In the mid-Sixties, some Western observers would have thought North Korea more 'democratic' (because less 'Fascist') than South Korea.  

For example, in the fourth century BC, Aristotle in Greece and Kautilya in India explored various possibilities of social choice in their classic books, Politics and Economics, respectively (the Sanskrit title of Kautilya’s book, Arthashastra, translates literally as “the discipline of material wellbeing”).

This is sheer nonsense. Aristotle thought that though the rule of the most able (timocracy) was a good thing. Democracy was evil because it was unlikely that those chosen by lot would be the most able.

 Kautilya served an Emperor and stressed the role of spies and a secret police keeping everybody under observation. On the other hand, he did consider Economic questions- e.g how to increase the tax yield without driving away productive classes- because that was what guys like him were paid to do. The choices made by Kings or Emperors are Sovereign rather than Social choices. The recommendations of priests or pedagogues are ethical and soteriological. They can be wholly independent of what obtains as Society.  

The two main insights of modern Social Choice theory- viz that no voting system is strategy proof and that 'agenda control'- i.e. the ability to decide the order in which issues are decided, can enable to implement any outcome you want even if you lack a majority for it- were always known to people since ancient times. Every ancient culture had instructors in rhetoric who taught students how to achieve their objective by exploiting 'cyclicity' by 'framing' the question differently. 

Pliny the Younger describes how he and his pals were able to get a freedman accused of killing a Senator acquitted by fits getting the issue of punishment addressed first. They disingenuously insisted that this should be execution, not banishment and got a majority for this result. This meant that people who would have voted for banishment, had to vote for acquittal. 

The arbitrary aspect of 'agenda control' is one reason why Social Choice via voting procedures is generally  subject to review or other types of countervailing power. Assemblies and Juries can do crazy shit. Rhetoric is a type of 'lawful magic' against which professional Politicians and Jurists are careful to find defenses. 

The study of social choice as a formal discipline first came into its own in the late eighteenth century, when the subject was pioneered by French mathematicians, particularly J. C. Borda and Marquis de Condorcet.

There had been plenty of very sophisticated voting systems in previous centuries. The Venetian one was particularly complicated. But who gets to be the Archbishop or the Doge or even the President of the Republic can be wholly irrelevant as far as the choices the Society is making is concerned. Voting rules are about avoiding conflict. They may attempt to 'bake in' a power-sharing arrangement of an elitist or undemocratic kind. But they still won't be 'strategy proof'. In any case, the really important decisions- how to defend the country or conquer other countries- aren't taken by rhetoricians or armchair philosophers. Either a 'Man of Destiny' rules the roost or else a particular coalition of vested interests prevails. 

Condorcet, it must be said, did have a vision of a utopian type of society. But it was Malthus's rejoinder to him which changed the direction of the Social and Life Sciences.  But this meant that the focus shifted from choices to the fitness landscape upon which choices are made. 

The intellectual climate of the time was greatly influenced by the European Enlightenment, with its interest in reasoned construction of a social order, and its commitment to the creation of a society responsive to people’s preferences.

The Enlightenment, sadly, was Racist. Even if it believed in Peace in Europe, the price would have to be paid by the conquest of non-European polities. Liebniz's 'perpetual peace' was based on France conquering Egypt. 

It should also be emphasized that though the Enlightenment was anti-Clerical and could be against Monarchical Absolutism, it was never for the 'great unwashed'. The people's preference was for more food and wine and holidays and killing Jews or other despised minorities- including fancy-shmancy intellectuals. 

But the theoretical investigations of Borda,

Borda merely rediscovered Cardinal Nicholas of Cusa's voting method which had been briefly considered in 1433 as a method for selecting the Holy Roman Emperor. There is nothing greatly wrong with the Borda method. It just isn't a panacea for anything because voting never is. 

Condorcet, and others often yielded rather pessimistic results.

But everybody already knew- just from playground debates at the age of 10- that voting doesn't have any magic powers. 

For example, the so-called “voting paradox” presented by Condorcet showed that majority rule can reach an impasse when every alternative is defeated in voting by some other alternative, so that no alternative is capable of standing up to the challenge of every other alternative.

But kids already know this by the time they are 10 years old. Once you get arguing over what game to play, the entire recess can pass without any game being played. All you have is a futile argument. Thus what happens is that a couple of kids start playing a particular game and there is a mimetic effect. Other kids join in. The arguers have to stand on the edge of the playground talking heatedly to each other. This gains them the reputation of being shit at games. The other kids say mean things about them.  

Social choice theory in its modern and systematic form owes its rigorous foundation to the work of Kenneth J. Arrow in his 1950 Columbia University PhD dissertation. Arrow’s thesis contained his famous “impossibility theorem,” an analytical result of breathtaking elegance and reach.

It was nonsense. Mathematically, it may be the case that a particular guy always votes for the winning candidate in every election. This does not mean he is 'decisive' over the outcome. The thing is a fluke. Arrow calls a guy of this sort a 'dictator' but he is no such thing. 

Arrow’s theorem shows that even very mild conditions of reasonableness in arriving at social decisions on the basis of simple preference rankings of a society’s individuals could not be simultaneously satisfied by any procedure.

It is unreasonable to think that anyone would accept a Social Choice rule. Alternatively, we could say 'the Social Choice rule we all accept has two components-

1) the Rule is to have no Rule

and

2) implementation of the Rule must occur when flying pigs prove the Reimann hypothesis , travel back in time, and give me a big sack of gold five minutes ago. 

When the book based on his dissertation, Social Choice and Individual Values, was published in 1951, it became an instant classic.

It was part and parcel of a rebellion against Government control of the Economy. Bureaucrats were making choices for the people and life had become grey. Eisenhower was elected President while, in England, the Tories returned to power.  

Economists, political theorists, moral and political philosophers, sociologists, and even the general public rapidly took notice of what seemed like – and indeed was – a devastating result.

Sen exaggerates the impact of Arrow's work. It was other writers- Ayn Rand, Raymond Aron, Arthur Koestler and even Karl Popper- who had an impact. Meanwhile, Anti Communist propaganda was becoming more and more sophisticated and better and better funded.  

Two centuries after visions of social rationality flowered in Enlightenment thinking, the project suddenly seemed, at least superficially, to be inescapably doomed.

Revolutions and 'Men of Destiny' now looked like a very bad idea. What people really wanted was affluence not some crazy type of enlightenment.  

It is important to understand why and how Arrow’s impossibility result comes about.

It comes about by telling a stupid lie- viz a guy who, by fluke, always votes for the winning candidate is secretly a Dictator.  

Scrutiny of the formal reasoning that establishes the theorem shows that relying only on the preference rankings of individuals

is stupid because no individual actually has such a preference ranking. There are billions of alternative social states and no individual has a knowledge of even a tiny fraction of them.  

makes it difficult to distinguish between very dissimilar social choice problems.

If you rely on something which does not and can not exist, your big problem is that you are a fucking moron.  

The usability of available information is further reduced by the combined effects of innocuous-seeming principles that are popular in informal discussions.

Each of those principles is crazy.  

It is essential, particularly for making judgments about social welfare, to compare different individuals’ gains and losses and to take note of their relative affluence, which cannot be immediately deduced only from people’s rankings of social alternatives.

But, if we actually had preferences over all social states then we would know what our judgments were. I could find out whether I believe String Theory could work by seeing what proportion of the Scientific Research budget I wanted allocated to that type of inquiry.  

It is also important to examine which types of clusters of preference rankings are problematic for different types of voting procedures.

But we would also have preferences over what proportion of the Social Choice Research budget should be spent on different 'problem areas'.  

Nonetheless, Arrow’s impossibility theorem ultimately played a hugely constructive role in investigating what democracy demands,

Nonsense! The thing was worthless. Democracy is the system of government which prevails if no other type of regime can be imposed. This is the case even if the majority would prefer a Monarchy or a Dictatorship. If would-be King or Dictator can kill off his rivals, we are stuck with Democracy.  

which goes well beyond counting votes (important as that is).

Sadly, Democracy does not disappear even if there is widespread electoral malpractice, voter suppression etc.  

Enriching the informational base of democracy and making greater use of interactive public reasoning can contribute significantly to making democracy more workable, and also allow reasoned assessment of social welfare.

But the same is true of Monarchy or Dictatorship.  

Social choice theory has thus become a broad discipline,

It has become an oubliette where useless tossers are dumped. Indian economists went in for it in a big way because India's economy had turned to shit thanks to Indian economists.  

covering a variety of distinct questions. Under what circumstances would majority rule yield unambiguous and consistent decisions?

Never. Decisions should not be 'consistent'- i.e. transitive- because the fitness landscape changes unpredictably and, in any case, is imperfectly known. The meaning of any decision will always be ambiguous because it could have been prompted by different considerations. We might say 'Country X decided to attack Country Y because X felt it was strong'. But it frequently happens that weakness sparks aggression. The hope is that the other side panics and yields.  

How robust are the different voting procedures for yielding cogent results?

All 'results' can be seen as cogent or utterly crazy depending on your point of view. Robustness simply means whether the thing survives when circumstances change. Britain and America have robust constitutions. France is on its Fifth Republic. Might Macron usher in a Sixth Republic?  

How can we judge how well a society as a whole is doing in light of its members’ disparate interests?

Are smart people entering or exiting that Society? If you compare the material standard of living of the median individual in different countries, you get an idea of how well different societies are doing. No doubt, some stupid Professor may claim that the people of Venezuela are much happier than the people of Canada. But Venezuelans want to emigrate to Canada. Canada may be boring but it is safe and prosperous. 

How, moreover, can we accommodate individuals’ rights and liberties while giving appropriate recognition to their overall preferences?

We only know about 'revealed preferences'. Are people running away from one place and flocking to another? Indians probably have more 'rights and liberties' than the people of some Oil rich states. Yet, Indians are very happy to relocate to where they will be better paid.  

How do we measure aggregate poverty in view of the varying predicaments and miseries of the diverse people who comprise the society?

If we are paid to say 'under this administration, poverty has risen', then we will fudge the numbers to prove that result.  

How do we arrive at social valuations of public goods such as the natural environment?

If we are paid to say that we are all going to die horribly within six months because of an ecological catastrophe, we will fudge the numbers to prove this assertion.  

Beyond these questions, a theory of justice can draw substantially on the insights and analytical results emerging from social choice theory (as I discussed in my 2009 book The Idea of Justice).

Sen confused 'Policy' with 'Justice'. The former is welcome to look at Market Research surveys of voters' preferences. The latter must not do so. It is enough if there is a Jury which makes determinations of facts on the basis of what reasonable people would consider to be true or right.  

Furthermore, the understanding generated by social choice theorists’ study of group decisions has helped some research that is not directly a part of social choice theory – for example, on the forms and consequences of gender inequality,

Male rapists should be sent to women's prisons if they say they feel they are actually women.  

or on the causation and prevention of famines.

Famines are caused by food availability deficit. Preventing them involves boosting the supply and transport of food. Sen's work is mischievous nonsense.  

The reach and relevance of social choice theory is extensive.

It is wholly useless.  

Rather than undermining the pursuit of social reasoning, Arrow’s deeply challenging impossibility theorem, and the large volume of literature that it has inspired, has immensely strengthened our ability to think rationally about the collective decision-making on which our survival and happiness depend.

While Sen-tentious cretins have been virtue signaling, China has risen and risen. It has made rational collective-decisions- e.g. imitate what more successful countries are doing- but it is an open question whether it can, sui generis, take the lead in technology. 

Thinking rationally involves rejecting stupid lies. Social Choice Theory is founded on the absurd proposition that everybody has a preference regarding everything. It ignores Knightian Uncertainty and the ubiquity of 'Tardean mimetics'. It refuses to recognize that what makes collective decisions possible is 'transferable utility'- i.e. bribes and threats.