Sen-tentious social Choice

 In his book 'An idea of Justice' Amartya Sen writes-

In formulating the problem of social choice based on individual preferences, Arrow took the viewpoint (following what was by then the dominant tradition) that ‘interpersonal comparison of utilities has no meaning’. The combination of relying only on individual utilities and denying any use of interpersonal comparison of utilities had a decisive role in precipitating the impossibility theorem.

If Sen is correct, then Arrow's theorem has no real world application save perhaps to machines. Human beings have preferences or utility functions which are not at all independent of each other. What we want changes depending on whom we are with and how they will be affected. If human beings did not have this quality, we would not be social animals and would probably have have ceased to exist as a species.

Sen's own idea is that 'interpersonal comparisons of Utility'- i.e. a common metric for measuring pleasure or strength of preference- provides a way out of Arrow's impossibility theorem which essentially says that no voting rule has certain desirable properties.

However, any 'interpersonal comparison of Utility' could be reflected in people's preferences profiles because they may choose what they consider best for Society, all things considered. In other words, if people want a voting rule to work in a particular way they could ensure it happens. If they don't, then that is their preference. There is no way to force the thing on them- which makes sense, because we are speaking of Choice, after all.

Let me illustrate an aspect of this difficulty. Consider, for example, the problem of choosing between different distributions of a cake between two or more persons. It turns out that in terms of informational availability in Arrow’s 1951 framework, we cannot, in effect, be guided by any equity consideration that would require the identification of the rich vis-a`-vis the poor. If ‘being rich’ or ‘being poor’ is defined in terms of income or commodity holdings, then that is a non-utility characteristic of which we cannot take any direct note in the Arrow system, because of the requirement to rely exclusively on utilities only.

 If people were interested in equity then they would derive more utility from equal shares. If some people are older and others are kids with a sweet tooth, the distribution might be between only the kids.
People could ensure that their preferences permitted the outcome they wanted.
However, because we are speaking of the free choice of a set of people, it would not be possible to impose some division upon them in the name of equity.

But nor can we identify a person’s ‘being rich’ or ‘being poor’ with having a high or a low level of happiness, since that would involve interpersonal comparison of happiness or utilities, which is also ruled out.

We can't do that anyway because the thing is false. Happiness has nothing to do with being rich or poor.

Equity considerations basically lose their applicability in this framework. The extent of happiness as an indicator of a person’s situation is applied to each individual separately – without any comparison between the levels of happiness of two different people – and no use can be made of the happiness metric to assess inequality and to take note of the demands of equity.

We do use a 'happiness metric' all the time. When I pass by a crowd of people leaving a cinema theatre who are beaming with happiness then I am inclined to buy a ticket to see the same film. On the other hand, if I see people leaving a restaurant clutching their tummies and vomiting and howling with distress, then I am inclined to dine elsewhere.

However, happiness has nothing to do with Wealth or 'the demands of equity'. That is why, as a species, we don't use a happiness metric to measure wealth or to redistribute income. It would be crazy to tax the poor but happy so as to further enrich the wealthy but miserable.

All this informational restriction leaves us with a class of decision procedures that are really some variant or other of voting methods (like majority decision). Since they do not need any interpersonal comparison, these voting procedures remain available in Arrow’s informational framework. But these procedures have consistency problems (discussed in Chapter 4), as had been noted more than two hundred years ago by French mathematicians such as Condorcet and Borda. For example, an alternative A can defeat B in a majority vote, while B defeats C, and C defeats A, all in majority voting. We are left, then, with the unattractive possibility of having a dictatorial method of social judgement (i.e. handing it over to one person, the ‘dictator’, whose preferences could then determine the social rankings). Dictatorial decision-making may, of course, be ferociously consistent, but that would be clearly a politically unacceptable method of decision-making, and it is in fact ruled out explicitly by one of Arrow’s conditions (that of ‘non-dictatorship’).

Sheer nonsense! Suppose there is a guy whom we all know to be smarter and more benevolent than any of us. We could delegate social choice to him. He wouldn't be a dictator at all. Arrow's theorem is a pile of shite because it defines anyone who arrives, by non-deterministic means, at the same result as the 'perfect', deterministic, voting procedure, as a Dictator even if they have no power and are wholly anonymous.

This is how Arrow’s impossibility result emerges. A number of other impossibility results were identified soon after, largely under the shadow of Arrow’s theorem, with different axioms but yielding similarly discouraging conclusions.

Arrow thought he had put paid to Bergson's Social Welfare Function but he was wrong. The fact is a guy with expert knowledge and benevolent intentions is trusted by ordinary people to choose for them. This does not make him a dictator any more than a Heart Surgeon I have freely chosen is actually a dangerous criminal because he cuts into my flesh with a knife.

It is true that it is a waste of time to find out what a person's utility function actually is. I don't myself know my own utility function. It is not worth my time to find out. I prefer to 'crowd source' or take expert advise when it comes to costly purchases.

Interpersonal comparisons of utility have to be made by judges and administrators and politicians. They may ask for expert testimony or rely upon market research or follow previous best practice.

This does not mean it is worthwhile to construct a Social Welfare Function for Society. Aggregating so much information accurately is simply too costly and error prone.

The ways and means of resolving such impossibilities have been fairly extensively explored since those pessimistic days and, among other things, it has clearly emerged that enriching the informational basis of social choice is an important necessity for overcoming the negative implications of an information-starved decisional system (as voting systems inescapably are, especially when applied to economic and social issues).

By 'enriching' Sen means 'telling stupid lies'. As a matter of fact, India's voting system features 'reserved seats' for certain sections of Society. However, this does not seem to have helped them very much.

For one thing, interpersonal comparisons of the advantages and disadvantages of individuals have to be given a central role in such social judgements.

If stupid people, like Sen, make social judgments those judgments are bound to be stupid. They can make all the interpersonal comparisons they like but will still end up wrecking the economy and destroying the polity.

If utility is the chosen indicator of individual advantage, then it is interpersonal comparison of utilities that become a crucial necessity for a viable system of social assessment.

Nobody has calculated his own utility function. It would be a waste of time to do so. Society shouldn't waste resources doing stupid shite just coz some stupid pedagogue says so.

This is, however, not to deny that it is possible to have social choice mechanisms that do without any interpersonal comparisons ofadvantages or utilities, but the claims of such mechanisms in fulfilling the demands of justice are weakened by their not being able to compare the well-being and relative advantages of different people in congruent scales.*

Nonsense! South Korea implemented one type of mechanism. North Korea implemented a very different one. We can compare North Korea and South Korea. Millions of the citizens of the former have to be forcibly prevented from running away to become citizens of the latter.

A fool like Sen may not be convinced by a metric involving people voting with their feet. But that's what makes him a fool.

Alternatively, as was discussed earlier, the informational inputs in a social choice exercise in the form of individual rankings can also be interpreted in ways other than as utility rankings or happiness orderings. Indeed, Arrow himself noted that, and the nature of the debate on the consistency of social choice systems can be – and has been – moved to a broader arena through reinterpreting the variables incorporated in the mathematical model underlying social choice systems. This issue was discussed in Chapter 4 (‘Voice and Social Choice’), and indeed ‘voice’ is a very different – and in many ways a more versatile – idea than the concept of happiness.

'Exit' is less versatile but wholly conclusive determinant. If people say how much they enjoyed your party but head for the door within 15 minutes of arriving then you know it was a mistake to construct all the canapes solely out of dog turds.

The utilitarian calculus based on happiness or desire-fulfilment can be deeply unfair to those who are persistently deprived, since our mental make-up and desires tend to adjust to circumstances, particularly to make life bearable in adverse situations.

No utilitarian calculus can in fact be constructed to any useful purpose. It can't be unfair to anything because it can't exist. Sen's idea of Justice consists in saying mean things to a wholly imaginary shibboleth.

It is through ‘coming to terms’ with one’s hopeless predicament that life is made somewhat bearable by the traditional underdogs, such as oppressed minorities in intolerant communities, sweated workers in exploitative industrial arrangements, precarious share-croppers living in a world of uncertainty, or subdued housewives in deeply sexist cultures.

Why did Sen's people migrate from their ancestral home in Bangladesh?  They could have 'come to terms' with being an oppressed minority in an intolerant community. Instead they kept moving to greener pastures. 'Exit' matters. It is based on interpersonal comparisons of utility of quite a complex kind. But no calculus is actually constructed. Mimetic and network effects 'crowd source' the result.

The hopelessly deprived people may lack the courage to desire any radical change and typically tend to adjust their desires and expectations to what little they see as feasible. They train themselves to take pleasure in small mercies.

But run away when they have a chance. If they don't get the chance then they work in an increasingly sub-optimal manner. That is why the utilitarian wants to improve their living standards and life chances. Their productivity increases so the thing 'pays for itself'. Utilitarianism is about removing ignorance and prejudice and complacency and laziness. Sen thinks its about constructing a calculus. No doubt, pretending to have such a calculus- like pretending to have supernatural powers- may yield an advantage in the short run. However, sooner or later, the truth will out.

Perhaps Sen, as 'the Mother Theresa of Economics' thought this book of his would make rich people in the West care more about poor people. It has the opposite effect. It makes us think there is no point to helping the poor. Sen says we have a natural tropism towards Justice. We will help the poor because we yearn to remove 'remediable injustice'. But, if this is the case, then the thing will have already happened. Sen's book is worthless. We don't have to read a book called 'the idea of Nutrition' in order to remember our duty to feed ourselves. Yet, Sen says we have a drive,  similar to that of hunger, to help those who have less. Why, then, does he feel it necessary to write such a long book?
The answer is that he thinks some Dead White Males most of us have never heard of made some mistake in some books they wrote a long time ago. This lead to the whole world failing to help the poor. Suppose those same Dead White Males had made an error in their theory of Nutrition- suppose they said food should be shoved up the anus, not taken orally- then everybody would have starved to death.

Sen's book is a 'second order theory'. He is criticising 'first order theories'. But those theories have had no practical effect. They are simply an unimportant part of a particular pedagogic tradition. They are wholly disconnected from any 'idea of Justice'. By contrast, actual Judges have to make interpersonal comparisons of utility and decide equitable damages all the time. This is an idiographic, practical matter. Nomothetic theories can only show their own irrelevance.