Suppes-Sen & graded shitting on equality

Life involves coevolving processes, themselves having game theoretic dimensions featuring uncorrelated asymmetries, which can appear to act like a Parrando game- i.e. a sequence of 'losing bets' yet yields a 'win- or Brownian ratchet or even a 'Maxwell Demon' etc. No paradoxes are involved because no set or class or unique pre-order obtains. 

 This is because of Knightian uncertainty- i.e. lack of knowledge or possible states of the world. There is no way to measure this. Gaining more knowledge does not necessarily mean we have reduced Knightian Uncertainty overall (though it may fall for any specific purpose) because we now understand that there are far more possibilities than we had envisaged or can now envisage. 

On the other hand, we can apply measure theory to a parameter whose value is unknown. But this involves something like the 'Maximum Uncertainty Principle'- For any event, if there are multiple reasonable values that an uncertain measure may take, then the value as close to 0.5 as possible is assigned to the event. This brings out the relationship between our need to measure or rank things and our basic intuition of equivalence or equality as arising where differences are currently indiscernible. This also relates to our notions of what is fair or just.

If we assume that the 'natural' outcome is a 50/50 split then we can rank whatever obtains in terms of its distance from 'equality'. Thus if my g.f's last boyfriend had a 9 inch dick then my dick is equal in size to his because half of 9 is 4.5 inches and nobody can be entirely certain whose dick is currently in the lady in question coz she's an utter slut. 

I mention this because some Indian mathematical economists who understood neither math nor econ got tired of creating poverty in India and decided to move to where they might get paid a little more money to measure, if not poverty- because that no longer existed in any very pressing form- then inequality.

Amartya Sen was one such. Fifty years ago he wrote-

The idea of inequality is both very simple and very complex.

No. Inequality exists wherever the outcome is unjustifiably different for different people who are otherwise similar. In other words, the 'maximum uncertainty principle' applies. Looking at me and looking at Beyonce, we'd really have no good reason not to think that I'd be equally likely to be a munificently remunerated international sex-symbol and global super-star. We can now measure inequality in our society- which reflects on structural racism against elderly, talentless, Tambram men of repulsive aspect- by comparing my earnings with those of 'Queen Bey'. We could not do so if some uncorrelated asymmetry- e.g. my looking 'male' or 'old' or 'fat' or 'ugly as shit'- obtained such that for a pre-existing reason, peeps could be certain I wasn't a beautiful African American female superstar. 

More generally there may be different types of inequality- economic, epistemic, aesthetic etc, etc. But that does not make the idea of inequality 'complex' because every departure from equality is specific and decomposable in terms of a unique structural causal model. An intuition of interdependence or evidence of heteroscedasticity simply means the structural causal model is wrong. This is obvious if you can't use it to improve actual outcomes immediately. But, since people only care about what they have, this means the only thing which matters is getting closer to the unique SCM which optimally improves outcomes. Stop worrying about inequality.  Switch funding to alethic research which measurably improves outcomes. Get an idea of what tech breakthrough is needed to get a better SCM. That's it. The thing may involve 'kairos'- timeliness- but it is not inherently complex. What is utterly simple-minded is the notion that, absent a better SCM, higher Math can come to the rescue.

 A lived experience of perfect equality may stimulate some higher mental state. Equally, it might be achievable by a brain damaged chimp. Equality is like that. It is multiply realizable. However there is a unique SCM which fully explains any actual inequality. One caveat. Uniqueness here refers to a specific Gentzen calculus not a general Hilbert one. But an SCM includes an explanation of how it itself proceeds. This can yield a 'canonicity' result by 'choice sequences' as used by Turing. As I have observed elsewhere- Overlapping choice sequences can define a co-evolutionary finitary fitness landscape corresponding to approximable reals.

Turning to the applications of ideas of equality- i.e. the ways we can generate a sense that inequality obtains or, alternatively, generate metrics for competing prescriptive SCMs- we find these may be very numerous indeed but that is because the idea of equality is very simple, not to say Tarskian primitive. The question is whether such applications are useful at this time. In Maths, a simple idea can have very useful applications. It can generate new and surprising knowledge simply through the very careful use of inductive reasoning. However, if stupidity, ignorance or craziness motivates ideas of equality- e.g. my claim to be equal in dick size to my g.f's last lover or my claim that Society unjustly discriminates between me and Beyonce- then knowledge of states of the world is being artificially reduced so that a 'Maximum Uncertainty Principle'- i.e. the notion that two things are equal because we have no reliable knowledge to otherwise distinguish between them- has purchase. This is just silly. Sen, of course, has devoted his career to being silly. But it is by pretending that his silliness is dictated by the great cognitive complexity of the subject matter that he has established his academic credentials. 

This is not to say that Maths has not progressed thanks to inequality results. The first systematic exploration of the subject was Hardy, Littlewood & Polya's 1934 book titled 'Inequalities'. The example they open with is the Cauchy inequality- viz. the square of the product is less than or equal to the product of the squares- whose generalization leads to a notion of a canonical 'norm' which establishes a non arbitrary measure of distance- i.e. a scalar representing an inner product. However, there is no uncertainty in the specification of the vectors involved. The work done by 'inequalities' here relates to giving a measure of distance which everybody would agree is 'natural' and which conveys useful information. Moreover, there is an empirical interpretation or concrete model which is subject to improvement. Thus, my smartwatch can tell me how many kilometres I've walked no matter which direction I chose to proceed in. This relates to the number of calories I've burned up. The relationship is not perfect. If I walk over hilly terrain, I burn more calories. But this is something that can be compensated for. I may find that walking up and down hills means I burn 50 percent more calories than when I walk an equal distance on level ground. Thus an hour's walk on Hampstead Heath is at least as good as an hour and half's circuit of Hyde Park. This does not mean that Hampstead Heath is one and a half times better than Hyde Park. It just means that for some specific purpose they are comparable in a useful manner. 

It should be emphasised that there is no point making comparisons just for the sake of it. All that matters is the next best alternative because it is coevolutionary processes, not some more unknowable phase space, that define the fitness landscape. 

 Patrick Suppes believed that a 'grading principle' could structure preferences such that utility maximisation occurred. He didn't get that if a 'primitive' we call utility to solve a coordination game exists, it must do so because it co-evolved with other things, none necessarily adjoint to it. But, even in that case, if we need a grading principle to add useful structure, why not have a grading grading principle and so forth? Either utility is whatever preferences 'reveal' or else utility is something better known to mathematicians- which is hilariously false. 

Suppes wrote in 1966 -  'it is a mistake to hold that grading principles aid us directly in distinguishing between the quality of acts. The function of grading principles is rather to aid the individual in constructing his preference relation on the set of consequences.' Thus, the 'logical status' of the grading principle is a 'binary relation' yielding a strict partial ordering on the set of consequences. However, it is illogical to have such a grading principle. Firstly, utility- being related to pleasure, pain, satisfaction etc- is coevolved. It helps us to figure out how to change the consequence set by figuring out how to make stuff more useful. Secondly, preferences are an information structure of a decentralized type. By Witsenhausen's counterexample, they are sub-optimal. Grading principles thus represent a type of inertia, or conatus, which is not really concerned with 'discovery' or the larger configuration space which their application would mischievously misrepresent. 

 Suppose you can either go to work today or not go to work. The consequence of going to work is your life carries on as normal. The best case of your not going to work is you get a tongue lashing from the boss and are docked a day's pay. That's all you need to know to decide to go to work. You don't need a strict partial ordering over the world in which the consequence of your bunking off is ranked higher in that you end up giving beejays at a truck stop rather tan taking it up the ass. Obviously, this isn't the whole story. Getting sacked from a job you hate may be the wake up call you need. What happens next is 'discovery'. This is why grading principles are useless. Logic says that the null set is the grading principle of the utility maximizer. Sen compounded Suppes stupidity so as to yield the utterly ridiculous 'Suppes-Sen' grading principle, a criteria of impartiality, 'Anonymous Pareto', in distributive justice, whereby a utility path dominates another if a finite permutation of the former Pareto dominates the latter. This is equivalent to first order stochastic dominance for a weakly increasing function. The problem is, some utility is always self-produced and necessary to preserve conatus- i.e. for the agent to continue to exist. But other utility is gained by changing conatus. This means who gets what when always matters. By contrast, the total payoff may not matter at all. Not everything is scarce at every moment. The relationship between utility and 'felicity functions' simply isn't what stupid Professors assumed. 

 The question we may well ask about shitty grading principles is- what is the 'empirical interpretation'? What are the ‘coordinating definitions’ giving rise to a ‘hierarchy of models’ between the theory and the experimental results? We don't know. The examples which the Professors come up are shit because the outcome set is clearly larger than they think because they are simply stupid. But nobody cares- more especially those in that shitty line of work. 

What is the origin of Suppes-Sen type stupidity? The answer is that it arises out of an inequality originally reported by Hardy &c such that for any continuous increasing function of a certain type, for two relevant vectors, an inequality must hold for permutations on those vectors. This is because their inner product space, under any permutation, is still a subset of that upon which the function is defined.

 Why might this matter? Well, to take a simple example, during lockdown, I might want to figure out how many times I need to climb the stairs and how much time I need to spend on the treadmill so as to duplicate the calorie burning effect of the walk on Hampstead Heath which I can no longer take. Climbing stairs isn't the same thing as walking up a hill but there is a way to find a non-arbitrary 'norm' such that my purpose is served. This does not involve any dominance relationship. It is not predicated on preferences . 

Inequalities in econ, like those in other 'applied' fields, can generate useful results. They point us towards finding things which are 'as good', not equivalent, for specific purposes. In econ, this is called substitutability. Perfect substitutability means infinite elasticity which means no 'unjust' exploitation or rent extraction can take place. Outcomes are equal once relevant differences are taken into account simply by the magic of the invisible hand.

But this result arises not by introducing some further mathematical refinement but just applying bog-standard econ which simply reduces to supply and demand. It is obvious that many people like watching a talented and beautiful woman twerking.  Nobody wants to see a fat elderly Tambram wiggling his buttocks. Stuff like that is empirical and simple enough in its way. It is foolish to appeal to some higher math in the belief that there is some more complex level to reality such that the fact that Beyonce is rich proves I gotta big dick.

 Suppes was smart but his theory of measurement only has purchase where there is a 'non-arbitrary' way to reduce things to numbers. I may say 'there is nothing arbitrary about my discovery. You too would assert it where you in my position- i.e. had a tiny todger.' But that is the definition of arbitrary! Some peeps got tiny dicks. Many don't. Still, anybody who doesn't agree with me is a fucking Fascist and probably votes for Trump or Modi or BoJo or some other such evil bastard. I suppose by bracketing Suppes with Sen, you get the diversity angle. If you say Suppes-Sen is nonsense - then you iz racist innit? I'm not racist because I'm genuine Tambram- i.e. not just educationally backward but mentally fucking retarded. Indeed, the only reason I write this blog is because I'm campaigning for affirmative action for Iyers on the grounds that most of us are Mani Shankar Aiyar level cretins. 

Sen is a high I.Q buddhijivi- but because, by Rothdard's Law, economists specialize in what they are least good at, he writes-

At one level it is the simplest of all ideas and has moved people with an immediate appeal hardly matched by any other concept.

No. Wanting nice shiny stuff moves people. Not getting nice shiny stuff which other peeps be getting moves the fuck out of people. Inequality does not. I don't care that you are of a different religion or race from me, nor even that you are smarter and better looking. I get angry if you get served something and I don't though we both paid the same amount of money for it.  

At another level, however, it is an exceedingly complex notion which makes statements on inequality highly problematic,

No. They are either true statements or false statements. There is nothing problematic about whether or not they have or lack verisimilitude.  

Sen says he wants to concentrate on economic inequality. But such inequality is wholly distributional. Why? Because economics looks at what happens to scarce resources. Who gets them? Why? Thus economic inequality can only be said to exist where there is a departure from an equal distribution of such resources. This departure may be 'justifiable'- e.g. guys doing horrible jobs have to be paid more so that they overcome 'disutility' from doing that horrible job. But it still represents inequality. 

Why does Sen say there is some 'complexity' here? He answers thus-

The measures of inequality that have been proposed in the economic literature fall broadly into two categories. On the one hand there are measures that try to catch the extent of inequality in some objective sense, usually employing some statistical measure of relative variation of income,

Which is all that can be done from the alethic point of view. An unequal real income distribution (which factors in leisure and imputed consumption of self-owned goods, talents, etc)  means there is economic inequality. We can then look at why this is so and tackle the underlying problem- e.g. reducing the disutility of some types of work or raising the productivity of other types of work or increasing mobility or creating better substitutes etc, etc.  

and on the other there are indices that try to measure inequality in terms of some normative notion of social welfare so that a higher degree of inequality corresponds to a lower level of social welfare for a given total of income.

But the reverse could just as easily be argued. We might say 'the slaves, or serfs, or whatever, are happier than us. They don't have to attend banquets and drink champagne. We must sacrifice our own digestions and our hope of Heaven to do the tedious work involved in an ostentatious life-style. 

It is possible to argue that there are some advantages in taking the former approach, so that one can distinguish between (a) ‘seeing’ more or less inequality

which is fine if it actually exists- i.e. our figures are accurate which they may not be if there is a large 'black economy'.  

, and (b) ‘valuing’ it more or less in ethical terms.

Why not do such 'valuing' in your own time? Economics is either a positive discipline or it is merely pi-jaw and virtue signalling.  

In the second approach inequality ceases to be an objective notion and the problem of measurement is enmeshed with that of ethical evaluation.

So don't do it- or do it in your spare time when you are getting drunk with your pals. 

This methodological point essentially reflects the dual nature of our conception of inequality.

We have no such thing. Either you are taller than me or you aren't. It is irrelevant that I think I ought to be taller than you because I am much fatter.  

There is, obviously, an objective element in this notion; a fifty-fifty division of a cake between two persons is clearly more equal in some straightforward sense than giving all to one and none to the other. On the other hand, in some complex problems of comparing alternative income distributions among a large number of people, it becomes very difficult to speak of inequality in a purely objective way,

Nonsense! Just plot the income distribution on a graph. Is it a horizontal line? No? Then inequality exists.  

and the measurement of the inequality level could be intractable without bringing in some ethical concepts.

Rubbish! Income inequality is like inequality of height. There is nothing ethical about it.  

Which of the two approaches it would be correct to pursue is not an easy question to answer,

Yes it is. Take the approach which is useful. Look at inequality of income and figure out how to reduce disutility and raise productivity or increase mobility and thus elasticity (thus eliminating 'rents) so that distribution improves from the perspective of every agent though the composition of the class of agents changes (fewer 'discouraged workers).  

and the two approaches in terms of their practical use would not be all that different from each other.

Sadly, saying women or minorities earn less and this is unfair does not actually help anyone except one or two 'token' hires or people in the public eye. 

Even if we take inequality as an objective notion,

which we can if we are economists 

our interest in its measurement must relate to our normative concern with it,

Nope. Economists are like Accountants. You hire them for a job or they do the job and then try to get funding for it.  

 To say that ‘x involves less inequality than y’,

is meaningless. Either x corresponds to more equal income distribution or it does not.  

even if meant to be a normative statement, will not imply an unqualified recommendation to choose x rather than y, but would presumably be combined with other considerations (e.g., those involving total income and such features) to arrive at an overall judgement.

Which would not be 'economic' at all.  

In one way or another, usable measures of inequality must combine factual features with normative ones.

No. If they are 'usable' for a positive purpose then they are positive, not normative. Telling lies, or claiming to have received a Revelation from God, is fine for any normative purpose.  

It is, however, possible to argue that the implicit notion of inequality that we carry in our mind is, in fact, much less precise and may correspond to an incomplete quasi-ordering.

Nonsense! We have an implicit idea of equality. We don't have an implicit idea of inequality as anything other than a departure from equality. Equality is not a 'quasi-ordering'. It a recognition that two things are the same for some specific purpose we are concerned with or from a point of view which has salience in that context. 

I have an implicit idea of 'beauty'. I may decide that two people are equally beautiful- e.g. Rachel and Monica on Friends. This does not mean I have any sort of quasi-ordering over ugly naked dudes in the apartments across the way. 

We may not indeed be able to decide whether one distribution x is more or less unequal than another,

but we can decide that, all things considered, they are equal. No remorse would be suffered by an 'antidosis'- i.e. an exchange between them. I'd be just as happy if I ended up with Rachel rather than Monica who may be high maintenance and a control freak but who is a professional chef. Food matters more and more as you get older.  

but we may be able to compare some other pairs perfectly well. The notion of inequality has many aspects,

No. It is wholly parasitic on the notion of equality.  

and a coincidence of them may permit a clear ranking, but when these different aspects conflict an incomplete ranking may emerge.

But nobody gives a fuck about such a ranking. We may care who wins a Beauty competition. We don't give a shit as to whether fat, ugly, naked guy is grosser than thin, ugly, naked guy. Sen, being Bengali, may live in a world where there is a Mister Ugly Naked Guy prize. We don't.  

There are reasons to believe that our idea of inequality as a ranking relation may indeed be inherently incomplete.

There is no reason to believe that we'd pay good money to have any such thing.

If so, to find a measure of inequality that involves a complete ordering may produce artificial problems, because a measure can hardly be more precise than the  concept it represents

Thus the fault of 'akriebia' arises in wasting any time on this. Economia, however, is concerned with inequality because it reflects something- disutility, productivity, factor elasticity- which we can do something about such that we all benefit. 

 How much guidance—it is reasonable to ask—can we expect to get from modern welfare economics in analysing problems of inequality?

Modern welfare econ is a branch of Public Finance. True there is a mathsy 'Social Choice' fringe but it is useless.  People in Public Finance- i.e. guys who work out how Governments should raise taxes and how they should spend that money- understand that they need to reduce the disutility of work for some groups while raising productivity for others and also raising labor elasticity of supply- e.g. improved mobility- such that 'exploitation' is lessened. 

The answer, alas, is: not a great deal. Much of modern welfare economies is concerned with precisely that set of questions which avoid judgements on income distribution altogether.

That's the mathsy masturbation Sen indulges in. But it has nothing to do with actual Public Finance or the type of Cost Benefit Analysis and Mechanism Design useful economists do.  

The concentration seems to be on issues that involve no conflict between different individuals (or groups, or classes), and for someone interested in inequality this can hardly make the air electric with expectations.

It should. By raising elasticity of supply- e.g ensuring that workers have a good 'next best' alternative- we eliminate Marxist 'exploitation'.  

The so-called ‘basic’ theorem of welfare economics is concerned with the relation between competitive equilibria and Pareto optimality.

He means the two fundamental theorems.  

The concept of Pareto optimality was evolved precisely to cut out the need for distributional judgements.

But Pareto is the guy who found 'power laws' in Income distribution. A Pareto improvement can worsen income distribution. This does not mean we should forbid it. On the contrary, we should work out why it did so. Chances are there is some way we can raise productivity or improve supply elasticity such that everybody would be better off. Consider what happens when I pay a guy to do my taxes coz I is innumerate. Invent an easy to use app so guys like me can do our own taxes and everybody is better off. Cretins become more productive and so the numerate guy who did my taxes can now move on to doing, higher value adding, more complex stuff in a booming economy. 

A change implies a Pareto-improvement if it makes no one worse off and someone better off. A situation is Pareto optimal if there exists no other attainable situation such that a move to it would be a Pareto-improvement.

But there always is such 'an attainable situation' in a real economy consisting of a goodly number of agents. 

That is, Pareto optimality only guarantees that no change is possible such that someone would become better off without making anyone worse off.

In other words, it merely forbids theft. There's smarter things we can be doing.  

If the lot of the poor cannot be made any better without cutting into the affluence of the rich,

the poor don't belong to the same species as the rich. If they do, there is always something which can be done to boost their productivity or raise their elasticity such that both the poor and the rich benefit.  

the situation would be Pareto optimal despite the disparity between the rich and the poor. Suppose we are considering the division of a cake.

Genuine economists aren't. Only buddhijivi wankers think it a smart idea to divide a cake before it is baked.  

Assuming that each person prefers to have more of the cake rather than less of it, every possible distribution will be Pareto optimal, because any change that makes someone better off is going to make someone else worse off.

This assumes distribution is wholly divorced from production. But then, there would be no cake.  

Since the only issue in this problem is that of distribution, Pareto optimality has no cutting power at all.

Yes it does. There is a pareto optimal cake size based on supply side factors. True, if 'snatching' occurs, then the cake may be smaller or non-existent. But 'snatching' is not a Pareto improvement. Furthermore, if a guy who would never have got cake still does not get cake there is no Pareto improvement or deterioration. 

The almost single-minded concern of modern welfare economics with Pareto optimality does not make that engaging branch of study particularly suitable for investigating problems of inequality,

But it does permit investigation of equality. Two states are indeed equal if both are on the Pareto frontier.  Suppose my stock-broker tells me that shares in Company A are as good as those in Company B. I buy A shares. Then I find out that the broker withheld information. Company B was going to merge with Company C. There was a Pareto improvement which he had knowledge which he withheld from me. I can sue him for damages because Company A and Company B weren't actually equal at all. B had the option of doing something mutually beneficial with C. 

Why does Sen himself use the Pareto condition? I suppose it is because he thinks Arrow's theorem wasn't nonsense.

r we impose five conditions on the relation f between individual preference orderings and social preference relation R.

Why do so? Why not just look at individual rankings of different Rs? After all, people have preferences over what type of Society they want to live in. These may conflict with what they currently prefer in the Society which currently exists. Thus I wear a suit rather than a frock to work. But I'd like to live in a Society where I could wear a dhoti to work. My preferences on R are what Society should take into account.  

Condition Q (Quasi-transitive Social Preference): The social preference R must be reflexive, complete and quasi-transitive, i.e., the range of f must be confined to preference relations R that are reflexive and complete and which involve a transitive strict preference relation P.

This is crazy shit. Every man may currently prefer to wear a suit and every woman a frock but it is perfectly possible that the majority of people may want a society where you could wear what you like.

Condition U (Unrestricted Domain): Any logically possible combination of individual preference orderings can be admitted.

Everybody wants there to be no fucking R which aint based on individual preferences re. R- i.e. we want Society to consider our preferences over what kind of Society we want rather than just focus on  our existing preferences as expressed in our daily behavior.  

Condition I (Independence of Irrelevant Alternatives): Social preference R over any pair x, y depends only on individual preferences over x, y.

But, we don't want Society to act in such a stupid way. It enjoys 'synergy'- i.e. the whole is more than the sum of its parts in the same way that assholes like me are more than the sum of our farts.

Society can find better alternatives than the suit/frock binary we have to put up with in day to day life.  

Condition P (Pareto Rule): For any pair x, y if all individuals find x to be at least as good as y and some individual finds x to be strictly better than y, then x is socially strictly preferred to y; and if all individuals are indifferent between x and y, then so is society.

That is a very stupid rule. Pareto spoke of 'derivations and residues'- i.e. stuff from the past which clutters up our social landscape. Why the fuck should I wear a tie? The thing is absurd. We want Society to clear away all such historical detritus so we can have better stuff on our menu of choice.  

Condition A (Anonymity): A permutation of individual orderings over the individuals keeps the social preference unchanged.

We don't want that. Some peeps be smarter and more socially aware. We want to know who they are and what they choose so that 'Tardean mimetics' improves outcomes.  

The first condition permits systematic social choice.

No. We would refuse to let Society chose stuff based on such a stupid principle.  

The second permits individuals to have any preference pattern.

Which is stupid. The whole point about learning to be smart is that you then chose in a smart manner. This should be widely known and emulated.  

The third establishes a relation between individual and social preferences that can be viewed pair by pair.

Which is silly. Nobody wants to view all sorts of silly alternatives 'pair by pair'.  

The fourth is simply the familiar Pareto rule. The last condition—originally introduced by May (1952) in the context of the simple majority rule—requires that no special importance should be attached to who in particular holds which preference, all that matters being the combination of preferences that are held (no matter who holds what). These conditions may look reasonable enough, but together they rule out distributional judgements in toto.

They also rule out Social Choice choosing anything Society would actually want. Thus all rational individuals would choose 'no Social Choice rule' and thus the nuisance would not exist.  

Theorem 1.1 The only functional relation f satisfying Conditions Q, U, I, P, and A must make all Pareto-incomparable states socially indifferent.

No. That relation f could map to the empty set- i.e. it could specify that Society should have no Preferences at all. Sen next provides an argument why this must be the case. 

There are various alternative ways of proving this theorem, and I give here the sketch of a proof which I have spelt out elsewhere. Define a person k as ‘semidecisive’  if his preferring any x to any y implies that socially x is regarded as at least as good as y.

We don't want Society to say anything of that sort. Currently we may have no interest in either x or y. But in the future one may be more useful to us than the other. Thus we don't want a 'stare decisis' type precedent of Society frowning on one or the other or saying they are equal for some purpose. Thus the fact that some k is just as happy eating chocolate cake as getting a whore to shit on him does not mean that we, at some future date, would be equally pleased if we were shat on by the waitress just because we ordered chocolate cake and Society has decided that being shat on was equally good. 

He is ‘almost semidecisive’ if xRy holds whenever he prefers x to y and furthermore everybody else prefers y to x. By using Conditions Q, U, P, and I, it can be shown that if a person is almost semidecisive over some ordered pair (x, y) then he must be semidecisive over every ordered pair.

Great! Suddenly we get shat on no matter what we order! 

Suppose there is Social Choice Rule liked by at least one agent. If it is implemented, that agent is 'semi-decisive'. Then under the conditions given above, that stupid fucker is semi-decisive over everything. We will spend a lot of time kicking him. That's why he himself will vote against it. 

Theorem 1.1 makes Pareto comparisons the only basis of social choice.

No. Pareto comparisons between possible states of the world are possible and they are the proper basis of social choice. We can see that everybody would be better off if we get rid of some binary choices- e.g. suit/frock- which are mere 'residues and derivatives' left over from the junkyard of history.  There are new possibilities which Science has opened up which we can only make actual by cohesive social action. In the process we can hit on a way that everybody benefits- or, at least, nobody loses materially such that Society becomes happier, wealthier and more secure.

That's what actual Social Choice is about. It isn't mathsy masturbation or virtue signalling. 

Since Pareto optimal points by definition are either Pareto-indifferent or Pareto-incomparable, they must all be declared socially indifferent.

No. There would be no Social Welfare Function under Sen's assumptions. Even the guy who came up with it would vote against its implementation once it dawns on him that everybody will blame him for everything and thus he will end up being kicked to death.  

Even if one person prefers one state to another—however mildly—and all others have the opposite preference, the two states must still be declared to be equally good from the social point of view given the axioms of Theorem 1.1.

No. Society can work out a way to pay off this guy or else it can find some stick to beat him with. Thus the 'hold-out' in one transaction can himself be the victim of 'hold-out' being used against him.  

We are back to a situation where judgements on inequality are not permitted

No. People can make what judgements they like. One such, is that what Sen has been doing is mathsy masturbation or rather, stupid, ignorant, shit.  

and Pareto optimality is both necessary and sufficient for overall social optimality.

Sufficient?! Is this man utterly mad? A situation where everybody starves to death may be 'Pareto optimal' because the guy with the can opener refuses to hand it over to the guys with the cans of food but it certainly isn't socially optimal.  

Anyone wishing to make distributional judgements must reject something or other in the framework of Theorem 1.1. Which of the five conditions is guilty?

All of them. They are foolish. Sen doesn't get that Society can do stuff which individuals can't do. We should look at the possible outcomes Society can achieve and identify something on the 'frontier' which everybody can get behind either because they would be better off or else because they would suffer a heavy penalty for being a hold-out. This is the sort of thing 'smoke filled committee rooms' can cobble together.  

I would argue that the real trouble lies in the very conception of a social welfare function, which makes social preference dependent on individual orderings only,

No. The problem arises because those orderings aren't over Socially feasible alternatives and mimetic effects, delegation, etc. are forbidden by stupid rules. 

using neither valuations of intensities of preference,

These don't matter. You may be violently opposed to Gay Marriage but you quieten down when we threaten to ban 'mega melons monthly'. I'm not saying this is the case with me. I'm talking about a bloke I know. I can't tell you his name coz we served in the SAS together. 

nor interpersonal comparisons of welfare.

i.e. making ignorant assumptions. It is all very well to say, the rich won't mind if we break into their house and drink some of the wine in their wine cellar. Those fuckers do mind. They employ goons who will beat the fuck out of us before handing us over to the coppers who will beat the fuck out of us before the judge sends us to jail where everybody will beat the fuck out of us and leave us with a prolapsed rectum. 

Avoiding interpersonal comparisons has been the dominant tradition in economics since the depression of the nineteen-thirties, for reasons that must have been—I suspect—unconnected with the depression itself, since the celebrated lambasting of interpersonal comparisons by Robbins (1932), (1988), and others, which started it all, could have hardly been inspired by the sight of obvious human misery.

Robbins explicitly mentions the Indian caste system and the notion that the Maharajahs need much more money because their capacity for satisfaction is much greater. 

He wrote- if the representative of some other civilisation were to assure us that we were wrong, that members of his caste were capable of experiencing ten times as much satisfaction from given incomes as members of an inferior caste, we could not refute him. We might poke fun at him. We might flare up with indignation, and say that his valuation was hateful, that it led to civil strife, unhappiness, unjust privilege, and so on and so forth. But we could not show that he was wrong in any objective sense, any more than we could show that we were right. And since in our hearts we do not believe that men are equally capable of satisfaction, it would really be rather silly if we continued to pretend that the justification for our scheme of things was in any way scientific. It can be justified on grounds of general convenience. Or it can be justified by appeal to ultimate standards of value. But it cannot be justified by appeal to any kind of positive science.

Robbins was writing this at the time of the Round Table Conferences in London. The arguments he refers to were actually being made. This group should have more votes than that group. Whites should be paid more than blacks. Women should be paid less regardless of color. All these arguments were based on 'interpersonal comparisons of utility'. 

The fact of the matter is that the Great Depression was caused by a monetary shock and then a collapse of aggregate demand. Raising taxes and doling out money to the unemployed was not the solution because the problem was not genuinely distributional at all. It was Keynesian. Why does Sen not know this? 

The point can be illustrated in terms of the exercise of dividing a cake of volume 100 between two persons 1 and 2, with y 1 + y 2 = 100, assuming that each prefers more to less. Armed only with individual orderings we know that person 1 prefers a 50–50 division to a 0–100 division, while person 2 prefers the latter.

If our task is to provide equal shares, then we cut the cake evenly.  Equality is easily achieved. Why bother ranking every type of inequality? Furthermore, there are many extraneous considerations- e.g. would one prefer we shat on their slice of cake? How about if we jizz on one piece but don't reveal which piece we jizzed on? How do we rank the different types of inequality which result? After all one guy may want the jizzed on cake. He picked the smaller piece because he was under the impression that our jizz was not strong and copious. Now he is crying his eyes out coz he can't taste no jizz. 

Now comparing the 50–50 division with a 49–51 division, we still have exactly the same ranking on the part of both individuals. We cannot say that the preferences were much sharper in the first case than in the second, since cardinality of individual utilities is not admitted; and this, combined with the ruling out of interpersonal comparisons, kills twice over any prospect of being able to make a statement of the kind that the gain of person 1 in going from 0 to 50 may be larger than the loss of person 2 in coming down from 100 to 50, or even from 51 to 50.

Sen understates the matter. We also can't say that person 2 is crying his eyes out coz we didn't jizz on his piece of cake. The beauty of making interpersonal comparisons of utility is that we can tell Sen that he'd be much happier if he ate only dog turds. Indeed, Society as a whole would be at least 5 trillion utiles better off if he ran after every dog in the street eagerly devouring any turds they might let drop from their anuses. 

Many rapists must feel hard done by for the refusal of Judges to entertain their 'interpersonal comparisons of utility' such that their own claim for payment by their victims are defeated and they are sentenced to prison for their altruistic habit of donating their sperm to people who didn't know their own cardinal utility function and thus expressed a wholly ignorant and unjustified resentment towards their benefactors.  

The ruling out of interpersonal comparisons even eliminates the possibility of our being able to say that person 2 is better off than person 1 under a 0–100 division.

Sen has now gone too far. We know that both 1 and 2 wanted cake. 2 got the cake. 2 is better off. How do we know? 1 will willingly exchange places with 2 but not vice versa.  

In fact all the characteristics of individual welfare levels in the distribution problem are precisely left out of account in this framework, and it is no wonder that a set of fine-looking conditions can complete the kill and eliminate distributional judgements altogether. Thus Theorem 1.1. 

There is no distribution problem. They guy who baked the cake owns the cake. The guy who didn't can pay for a slice or can ingratiate himself in some way with the other guy and thus get some cake. What Society can do is to find ways of increasing equality such that everybody gets the resources to either bake or buy an equal amount of cake- if that is what they want to do. 

 It seems reasonable, therefore, to argue that if the approach of social welfare functions is to give us any substantial help in measuring inequality, or in evaluating alternative measures of inequality, then the framework must be broadened to include interpersonal comparisons of welfare.

Inequality means 'not equal'. It is measured as a percentage deviation from equality. This has nothing to do with Social Welfare functions which may take such a measure as an argument but which don't themselves embody equality. They merely establish what can be done with a Society's resources so as to achieve Social Welfare. 

The question will be asked at this stage whether such comparisons are at all legitimate, and if so in what sense. Despite the widespread allergy to interpersonal comparisons among professional economists, it is I think fair to say that such comparisons can be given a precisely defined meaning. In fact, various alternative frameworks are possible. One in particular will be pursued here. If I say ‘I would prefer to be person A rather than person B in this situation’, I am indulging in an interpersonal comparison.

No. You are saying something about yourself. It may be true or it may be hypocritical or strategic. But just saying stuff of that sort doesn't mean you have made any sort of comparison involving the personalities of the people mentioned.  

While we do not really have the opportunity (or perhaps the misfortune, as the case may be) of in fact becoming A or B, we can think quite systematically about such a choice, and indeed we seem to make such comparisons frequently. Representing (x, i) as being individual i (with his tastes and mental qualities as well) in social state x, a preference relation defined over all such pairs provides an ‘ordinal’ structure of interpersonal comparisons.

Social state x already contains all compossible individuals with their tastes and mental qualities and sexual peccadillos.  We don't know, for any i, whether their existence would be compossible with state x. The dude may have starved to death or emigrated. More generally, i is not independent of x. Our tastes are shaped by the society we live in. 

A binary relation associates one element from one set to an element of another set. If this generates a unique 'pre-order' we are on our way to establishing a metric- i.e. being able to say how far or close things are- e.g this state of society is taking us farther away from equality. But we need to chose that binary carefully and so as to satisfy 'nautrality' or 'canonicity'. An arbitrary 'binary relationship'  is quite useless. Every asshole has a different one. 

Furthermore, we don't know if states of the world are finite or infinite because 'tastes' may be impredicatively or intensionally defined such that they have an infinite extension. This means we don't know if there is 'preference relation' or unique pre-order. Simply assuming it exists is like assuming that there is a way to turn everything in the Universe into strawberry jam. 

To obtain interpersonally comparable cardinal welfare levels, one would have to go beyond such a ranking and introduce additional features for the sake of cardinalization.

This can easily be done by turning the Universe into strawberry jam. 

Utilitarianism is egalitarian in that the aim is to maximize hedonic pleasure, utility and satisfaction. Since it is true that beyond a certain point, there is diminishing satisfaction from extra consumption, it follows that goods and services will be distributed in a more equal manner by a Utilitarian Society. 

Sen takes the opposite view- 

 utilitarianism (has an)  ill-deserved egalitarian reputation... the true character of that approach can be seen quite easily by considering a case where one person A derives exactly twice as much utility as person B from any given level of income, say, because B has some handicap, e.g., being a cripple.

This is an ignorant and bigoted statement. Handicapped people have as much vitality and love of life as dusky folk or dudes wot don't have dicks but got veejayjays instead.  

 In the framework of interpersonal comparisons outlined earlier, this simply means that the person making the judgement regards A's position as being twice as good as B's position for any given level of income.

No. It says B suffers disutility even at leisure. By figuring out a way to reduce that disutility we increase total Utility. This may also enable B to earn much more money than A because he is now mobile.  

In this case the rule of maximizing the sum-total of utility of the two would require that person A be given a higher income than B. It may be noted that, even if income were equally divided, under the assumptions made A would have received more utility than B; and instead of reducing this inequality, the utilitarian rule of distribution compounds it by giving more income to A, who is already better off.

So, kids, what have we learned today? Economists are as stupid as shit. They don't get that people have preferences over what Society can achieve which in turn is qualitatively different from what can be done just by decentralized decision making. Society can pass laws, levy taxes and provide public goods. Some economists- Sen in particular- didn't get this. They wasted their time masturbating in a faux mathsy manner (pretending there was a unique pre-order when no such thing obtained) while completely ignoring the blindingly obvious fact that Welfare Econ is part of Public Finance and 'Law & Econ'. It has nothing to do with 'Social Choice theory' because nobody in their right mind would vote for the imposition of anything so stupid. 

Sen also shits on Utilitarianism- an ideology taken up by the founders of his own ancestral Brahmo Samaj- by suggesting that it didn't get that helping the handicapped reduce 'disutility' is good for everybody. Instead Sen thinks Utilitarianism is about paying the healthy twice as much for the same job as a 'cripple'!  Some people have suggested that Sen got a Nobel because he was brown. This is unfair. He got a Nobel because he was stupid- which was funny coz he was brown and came from a starving shithole where the cure for poverty and the case for equality were both so blindingly obvious that only a Cambridge PhD, teaching Econ at Harvard, could remain in ignorance of either.