Igersheim on the death of Welfare Economics

Do we choose the system of ethics- i.e. the value judgments- we consider ourselves as bound by, or is it imposed on us?

If we choose it, then it is merely a type of preference. If it is imposed it is merely a type of constraint.

In the former case, either we fail in upholding our system of ethics- i.e. at least one of our action guiding value judgments was disobeyed by us- or we don't and, according to our own criteria, are perfectly ethical. But this means we can always choose an ethical system such that no matter what we do, we are acting perfectly ethically.

In the latter case, where ethics is something imposed on us as a constraint, it would be sufficient to change whom we interact with such that the constraint is not binding- i.e. has no effect on our behavior- for us to be perfectly ethical. If this is not possible, it is still the case that our intention is ethical but the outcome, which is that we behave unethically, is not our fault. It is the fault of exogenous constraints.

Clearly, ethics itself mustn't say it is either based purely on individual choice or based purely on something imposed upon the individual. Why? It would immediately disappear as an area of discourse. Everyone would say- 'I'm perfectly ethical save by reason of exogenous constraints'.

Suppose Medicine says 'sickness' is not a 'primitive notion' which arises from the study of human bodies but rather is either a matter of individual definition or else its definition is imposed on the individual. Then everybody could choose to be healthy- and if they fail to do so are merely in what Christian Scientists term 'error' and perversely choosing to malinger- or else the imposed definition could be changed such that billions of people dying prematurely because of treatable medical conditions are all perfectly healthy but simply choosing to die for some personal reason.

In other words, Medicine would disappear as a Scientific discourse if it were so foolish as to surrender the proper use of its 'primitive terms' to people not primarily concerned with the scientific study of the human body- be they individuals or some Social structure which can impose a definition of sickness on individuals.

Economics did precisely that when it surrendered its primitive notion of 'choice' to Relation Algebra with the result that an abortion termed 'Social Choice theory' was hailed as the Messiah by some stupid Bengalis hoping to escape conscription into a corrupt and incompetent Planning Commission by emigrating to Ivy League Ivory Towers.

Just as 'sickness' and 'health' are primitive notions, or undefined terms, which naturally arise in the course of the scientific study of human bodies, so too is 'choice' a primitive term which arises when we look at how people allocate resources under scarcity. Medical professionals help heal human bodies. Professional Economists help human beings economize on the use of scarce resources- including their own time and cognitive effort.

In a country were a lot of people have well-paid jobs in Medicine, a few people can make a little money looking at statistics about Public Health. They can gain a bit of publicity for themselves by saying startling 'counter-intuitive' things- like poor people who have little access to health care are actually healthier than rich people. This can be done by ignoring the 'ceteris paribus' condition- i.e. by comparing apples with oranges or, to put it more technically, by treating populations with different characteristics as if they were identical. Moreover, some charlatans can give 'metaphysical' reasons for the superior efficacy of some nostrum of their own.

Similarly, in a country where a lot of people are well-paid because resources are allocated in a smart manner, a few academics can gain publicity and money for themselves by bogus statistical studies designed to generate a moral panic. Moreover, some charlatans can give 'mathematical' reasons for the superior morality of some mishegoss of their own.

A recent paper by Herrade Igersheim sheds light on 'the death of Welfare Economics'- in particular, that of Samuelson- and the birth of Arrowvian 'Social Choice theory.'

Samuelson, following an older 'organicist' tradition, held Ethics to be something imposed, not chosen-

Arrow- a student of Tarski's Relation Algebra- belonged to a younger cohort who, quite naturally, rejected 'organicism' and the racialist and ultra nationalitst politics it had, so recently, been associated with. He wrote circa 1952

in my book I have employed the expression social welfare function to designate what I call here social choice function. I. M. D. Little has shown that using the term ‘social welfare’ would make the reader believe that the ordering of social preferences which results from it constitutes a system of ethical judgements held by ‘society.’ I fully agree that value judgements can be held only by individuals […].

Legal judgments are not opinions 'held by individuals'. To be valid, they involve a protocol bound decision process which is wholly impersonal. An actual stare decisis judgment may reflect the preference of no individual whatsoever. Imagine the following case. Rufus Isaacs as Lord Chief Justice gives a judgment which he himself, having resigned that office, interprets in a particular way. He approaches the Bench, now as an ordinary barrister, to urge this interpretation. They reject it. It may be that each member of the Bunch rejects it for a different reason and that each has a different interpretation of it. Indeed, it may be that there is no man in England who agrees with any other as to the correct interpretation of a Judgment given by Rufus Isaacs as Lord Chief Justice.

Why should 'value judgments' be different from legal judgments? As a Smarta Brahman I consider the highest service to Society I am capable of performing to consist of making fun of Iyengars and hinting that they put garlic in the sambar. However, this 'value judgment' is not held by me. It arises out of the deliberations of a properly constituted, protocol bound, Smarta Vicharam featuring such luminaries as Nanotechnology Natraj Iyer, Atul Gopichand (an honorary Iyer by reason of his practice of farting and exiting the elevator anytime Amartya Sen entered it) and some other drunken fellow who joined our table and started singing in Punjabi.

Unlike purely personal preferences which reflect idiosyncratic features, our value judgments are nomothetic and defeasible in a more or less impersonal, protocol bound, manner. It is of their essence that they can't be held by individuals qua individuals but rather are attributed to some wholly impersonal adjudicating authority.

Arrowvian social choice functions deal with fixed preferences. They can't capture the nature of value judgments, which like legal judgments, are action guiding without being known in advance. Thus I may do something believing it to be legal only to find I was wrong. The Court did not take the view which my lawyer considered correct. Alternatively, I may do something I believe is wrong with the purpose of bringing a test case to clarify what I believe to be an ambiguity in the law. Something similar is true of our value-judgments. There is an experimental or investigative aspect to them. They do not represent preferences fixed over states of the world. Rather they are tools to pierce the fog of Moral Uncertainty.

Arrow, speaking with post-War optimism, disagreed

Nevertheless, the social choice function does have a very close formal  resemblance to the concept of the social welfare function introduced by Bergson some years ago; both functions define an ordering constructed by aggregation of individual orderings. 

Igersheim comments-

 In this 1952 paper, in order to illustrate how the B-S SWF is impacted by his result, Arrow presents an individual named Primus who has the difficult task to propose a new ordering both on the basis of his own ethical viewpoint and of the preferences of all the other individuals of the society. For the conditions Arrow states are “value judgments which might reasonably be part of the ethics of Primus”, Primus “will find […] that he cannot construct a preference scale which would express his ethical choices among various distributions and would be in accord with these value judgements” 

It is not reasonable to term 'Dictatorship' a situation where one person has the preferences which everybody would agree to be the best for Society. This was Samuelson's point.
The magic of the Spilrajn theorem is that, ex post, there must always be an infinite number of such possible 'Dictators' whom it would be 'Dictatorial' to exclude. Igersheim quotes Ian Little as making a similar point at the very inception of the controversy.

In this particular case, Primus can't assent to Arrow's stipulation because he knows he is himself free to choose 'value judgments' different from Arrow's. The fact that he may believe that any system of ethics he subscribes to could be defeated by Arrow does not restrict his choice menu at all. Arrow has stipulated that the Aggregating process be deterministic. We don't know that a non-deterministic process suffers from a like infirmity. There is no way to rule the possibility out. Indeed, deterministic processes with an 'intensional', or arbitrary,
type theoretic component are indistinguishable from non-deterministic processes.
Real life, protocol bound, judicial processes have this quality. There is no algorithm to determine Supreme Court decisions though parsing such decisions does involve deterministic reasoning.

As a matter of fact, not conjecture, some Law Professors find Arrow's theorem highly illuminating. But, it isn't a knock-down argument against anything. We have good reasons to believe that chanting some combination of Vedic verses won't cause the monsoon to arrive. But, we have no means to rule out the possibility. Still, Physicists and Meteorologists can refute any 'Structural Causal Model' put forward by old fashioned Purohits in this respect. What of Arrow's theorem? Does anything in our experience correspond to 'the Death of Welfare Economics' at the hands of something with a superior 'Structural Causal Model'- i.e. something which makes better predictions or allows us to have better, or at least more secure and comfortable, lives? No. All that happened was that some stupid academics got tenure rationing credentials signalling silliness and sycophancy for some stupid careerists and the Academo-Bureaucratic Ponzi schemes which employ them.

Igersheim ably traces the history of the wholly sterile Samuelson v Arrow debate. Reading her paper we see that both Arrow and Samuelson were making the same mistake. They thought preferences or choices in ethical matters involves scarcity, i.e. opportunity cost, and thus were subject to the law of the excluded middle. This is not the case. Ethics is investigative. Like Science or Art or Soteriology it has a notion of a felix culpa or something which is right because it is wrong. In ethics, new commodities are created ex nihilo. This is not the case in economics. In ethics, nothing is necessarily rivalrous or infeasible. Income and hedging effects can be infinite. This does not mean it is 'anything goes' in the manner of Arrowvian Economic 'general equilibrium' where Income effects or hedging behavior has precisely this effect.

Samuelson had a bee in his bonnet- or methodological shibboleth- relating to cardinal utility and 'interpersonal comparisons of utility'- though it is a mathematical fact that everything which is ordinal is also cardinally representable. Moreover, human beings are mimetic creatures who need to make 'interpersonal comparisons of utility' all the time so as to improve their lives or avoid catastrophic harm.

Arrow, it seems, thought that P=NP or as he put it back in the Fifties- '“the Bergson social welfare function is mathematically isomorphic to [Arrow’s] social welfare function. […] Hence, the Possibility Theorem […] is applicable here; we cannot construct a Bergson social welfare function”

Brouwer's work on choice sequences permitted precisely this possibility. Indeed, its 'intuitionism' was compatible with a type of 'organicism' which was more in the spirit of Pierce & Morgan & Lady Victoria Welby & an Evangelical Christianity of a genuinely irenic and Universalist sort.

Choice sequences are not deterministic. A Mathematics based on them does no have to accept the law of the excluded middle, or- in an Economic context- the notion of opportunity cost as attaching to Choice. One only needs to 'economize' if there is opportunity cost due to scarcity. But in ethics and politics scarcity does not always obtain. It is perfectly possible that a non rival, non excludable, merit good has zero cost of production.

Igersheim's paper gives a succinct account of developments in the Seventies- highlighting

papers by Parks and by Kemp and Ng... aimed at showing that “it is impossible to find a ‘reasonable’ Bergson-Samuelson SWF based on individual orderings” (Kemp and Ng, 1976: 59). In other words, according to all three scholars, a B-S SWF cannot exist without interpersonal comparisons, thus stressing the similarity of their impossibility theorem with Arrow’s conclusions.

Speaking generally, we buy stuff which we see other people buying and gaining utility from. We say- 'that guy is like me but he's much happier than me because he is eating a burger while I am eating grass'. 

A Social Welfare function is about identifying people who could gain by having nice stuff instead of shitty stuff. We don't have to be able to say 'this guy will gain x number of utiles from eating a burger rather than eating grass.' However, some nerd could make a computation and say that our actions are consistent with maximizing 'utiles' of the sort he computed. But the nerd does not matter. What matters is making life better for other people.

The basic idea of these papers is to adapt the conditions devised by Arrow when one considers that individual preferences are given, i.e., for a single profile of individual preferences. One can summarize this basic idea as follows: the condition of universal domain, the weak Pareto principle and the condition of non-dictatorship are stated in a slightly different way, but the real innovation is to devise a condition of neutrality, which is, according to the authors, the companion of the condition of the independence of irrelevant alternatives, but in the context of given individual preferences (Kemp and Ng, 1976: 61; Parks, 1976: 448). The condition of neutrality implies that the social welfare function treats all the alternatives the same way and can be stated as follows: if a particular subprofile of individual preferences for x against y results in a social preference for x over y, and the same subprofile of individual preferences holds for z against w, then z is socially preferred to w. At the end, it is shown that in these circumstances there is no social welfare function satisfying the four conditions.

 This and other similar work showed that ordinalism plus a ban on interpersonal comparisions renders Welfare Econ empty. This is scarcely surprising. If all we know is how people rank choices and nothing more then we can't say what Society should do. Thus, I might say- 'hey! Look at all those emaciated guys who are starving to death. Let us feed them some nice food. Then they will be happier and more productive and we'll all be happier.' You might reply- 'if we feed them, there will be a measurable difference in all sort of medical indices of their well-being. Thus, there could be a cardinal measure of utility. Moreover, we'd be making 'interpersonal comparisons' between well nourished people and starving people. This is not licit. How do we know that starving to death isn't highly desirable?

Igesheim next looks at the Pareto condition-

She quotes Samuelson as saying 'I recall that, at the NYU Sidney Hook conference on Philosophy and Economics, Kenneth Arrow startled the philosophers present (and me, too) when he declared something like: ‘Surely when all the individuals agree that situation A is better than situation B, any admissible ethical system must not second guess their desires.’ I don’t recall Bergson as ever going to that extreme.

If Arrow is correct, not only is Ethics empty but so is Social Choice theory because we can all agree that it has been wholly useless in helping Society to choose anything. 

Still, it is probably a good thing that Social Choice existed because it enabled India to get rid of a number of shitheads who might otherwise have joined the Planning Commission or pretended to be Marxists or 'Development Economists' or some other such oxymoron.

Closely scrutinized, the problem Samuelson encountered with Arrow’s use of Pareto optimality, i.e., in a multi-profile framework and whatever the modifications of the other “irrelevant” alternatives, seems to have some relationship with the “independence” property of the Pareto principle revealed by Sen in his “Paretian epidemic” (1976).

This 'epidemic arises' by, very stupidly, inventing something called a 'potential semi-right' and saying if a person has full rights over one thing then they have potential semi-rights over everything. Thus if you have a mustache you potentially have a vagina- indeed you potentially have countless vaginas. 

Indeed, according to Sen, an indefatigable detractor of the Pareto principle, notably through his liberal paradox (1970), this principle includes two features: a quite uncontroversial unanimous aspect saying that if everyone has the same preference over all the social states, then social choice should reflect it; and an “independence” property saying that the social choice over a pair must depend only on individual preferences over that pair (1976: 220). Of course, one cannot but point out that the latter feature has many similarities with the independence of irrelevant alternatives. Thus, Samuelson’s focus on Arrow’s Pareto condition is of the same kind as the criticisms formulated by Sen’s “Paretian epidemic,” but in a more intuitive and incomplete way. As such, it could simply be another way for Samuelson to express his disapproval regarding Arrow’s formalism. 

Samuelson had his foolish hangup over ordinality and Arrow had his foolish hangup about how a guy who isn't a Dictator is too a Dictator if he happens to want what's best for Society. Sen is the joker in the pack. His 'potential semi-rights' involve people with mustaches potentially being a large sack of vaginas. 

Igersheim concludes thus-  as recently pointed out by Hands (2014: 112), “Samuelson very seldom sheds any serious light on any of the relevant issues, and yet he seems continually compelled to say something.”

Change 'Samuelson' to 'Academics' and you'd be on to something. Those who can, do. Those who can't, teach.