Sunday 21 May 2023

Social Choice Theory & the idea of Justice

We, as individuals, if isolated from each other, find pleasure, or comfort, in things very different from the things which we prefer when we are in the company of our beloved family, or friends, or esteemed work colleagues. 

To some extent, there can be 'preference falsification' when we are in a group. We all agree to do things which none of us wants to do but which we assume others enjoy. I suppose there are also things we do in isolation which we don't really like but which are somehow associated in our mind with solitary behavior. This suggests that our preferences are 'intensional' or 'epistemic'. They change as our knowledge changes. To treat them as given exogenously is to commit the intensional, or masked man, fallacy. This means that no mathematical set or relation will be well defined in this connection. To attempt to use mathematical logic when it comes to individual or social choice is to generate stupid nonsense. 

The fact is, both as atomized individuals and as social beings there are somethings we need to do so as to continue to exist as such. As our knowledge improves, our ability to survive improves. We can make better- more useful, choices. The notion of 'utility' captures this notion. 

Individual preferences, considered in isolation, would not give us the information we need for a theory of how and what Society should choose. Indeed, this is an ideographic matter. It depends on the circumstances in which a particular Society finds itself at a particular time. This means that Society should adopt different policies at different times. Should it also have a different idea of justice under exigent circumstances? Perhaps. But there is a benefit in maintaining the prestige of judicial institutions and its customary protocols. Sentencing policy can always be changed and Special Courts can be constituted to speed matters up under exigent circumstances. Obviously, there is also the possibility of turning a blind eye to extra-judicial killing. Still, there is a slippery slope here and so, other things being equal, it is better to leave policy flexible while keeping a Society's idea and institutions of Justice relatively fixed such that they only very gradually or imperceptibly evolve and adapt.

One question Societies have to confront from time to time is how to reallocate property rights. The Social Contract, after all, is 'incomplete'. Of its nature, control rights have to be renegotiated or reassigned from time to time so as to maintain incentive compatibility, But this falls under the purview of 'political question'. It is a matter of Policy, not Justice. But that policy must look at the needs of Society- how it must change to survive- it can't be based on any individualistic moral intuition or conception of fairness. Social Choice must be made at the level of Society. Thankfully, ordinary people understand this. They decide matters differently when acting as representatives of a family or community rather than as individuals. This is true both in the market- Mums buy a different set of groceries than they would if they were carefree singletons- as well as when it comes to exercising their franchise.

Arrow had a very silly theorem based on the notion that people vote in the same way they shop when they are completely isolated. But few of us genuinely live isolated lives. We shop for our families and we vote for what is best for our communities and societies. Aggregating isolated, individualistic, preferences is pointless. Man is a Social Animal. Whatever method a particular Society has of making choices, there is some way some people in that Society can steer it to make good choices. 

Sadly, those people are unlikely to be philosophers. They will possess some modicum of common sense. 

Amartya Sen takes a different view. In 'Idea of Justice' writes- 

 In a letter to Paul Engelmann, written in 1917, Wittgenstein made the wonderfully enigmatic remark: ‘I work quite diligently and wish that I were better and smarter.

This is scarcely enigmatic. If you are working diligently, you will want to be better at your work and smarter in the way you approach it.  

And these both are one and the same.’ Really? One and the same thing – being a smarter human being and a better person?

Sen, it appears on the basis of what he says elsewhere, thinks that being a better person means working for the welfare for others. Perhaps, a smarter person can do more for others than a stupid person. The problem is that we know that neither Wittgenstein nor Sen have actually dedicated themselves to working selflessly for others. Both were academics. Wittgenstein is saying something 'imperative'. He wants to be smarter because that will make him better at what he was doing- which was philosophy of some Fregean kind. He is expressing his dedication to his self-chosen vocation. But, philosophy isn't really about selfless social service. 

Sen, in his book, is making the claim that Social Choice Theory can improve our idea of Justice. It can make us more inclined to selflessly serve others. Yet there is no evidence that Social Choice theorists have made the world a better place. They have simply written nonsense. Why? The answer is that they have followed Arrow in focusing on individualistic characteristics- whether they are 'preferences' or 'capabilities' or 'functionings'. Yet, what we do and what we chose as social beings are very different from what we could do or choose as isolated individuals. It is not the case that some mathematical function, or Government bureau, can replace our families and friends and neighbors and colleagues and the communities we have grown up in such that our actions are coordinated in a benign manner. 

Yet this is the utterly absurd motivation for Sen's fatuous work. 

As an evaluative discipline, social choice theory is deeply concerned with the rational basis of social judgements and public decisions in choosing between social alternatives.

This isn't true. Cost Benefit Analysis evaluates 'social judgments'. Such exercises may be mandated by law or administrative rules and regulations.  At the macro level, sophisticated econometric models may justify changes in fiscal or monetary or trade policy. But Social Choice theory has never been used to critique any actual economic decision by a government in any country. 

What is the 'rational basis' of making a social choice? Surely, it is a prediction about the consequences of the choice- who it will benefit, who will it hurt, and by how much? But this is just plain Economics or a type of National Income accounting. It isn't Social Choice theory at all. 

The outcomes of the social choice procedure take the form of ranking different states of affair from a ‘social point of view’, in the light of the assessments of the people involved.

But no such ranking has been produced by anybody anywhere! It is a different matter that there all sorts of Market research companies and professional psephologists who claim to have data on what particular voters at particular times want Governments to deliver. But this has nothing to do with Social Choice theory. There is no 'ranking' or 'ordering' of social states- which, in any case, are unknown. Smart politicians may be able to tailor benefits to specific groups so as to win particular elections. But there is a cosmetic aspect to this. The government may hand out cash with one hand while clawing it back through a less 'visible' tax with the other hand.  

This is very different from a search for the supreme alternative among all possible alternatives, with which the idea of justice theories of justice from Hobbes to Rawls and Nozick are concerned.

The 'supreme alternative' has nothing to do with Justice. For Ukraine, currently, the supreme alternative is defeating Putin's goons, recovering all its territory, joining NATO and the EU and growing rich through the hard work and enterprise of its own people.

Similarly the 'supreme alternative' for America is to be once again the mightiest and richest and most scientifically advanced nation on the planet. 

This is what Politics is about. Nobody cares about Hobbes or Rawls or Nozick.  

The distinction is important, for reasons that have already been discussed in earlier chapters. A transcendental approach cannot, on its own, address questions about advancing justice and compare alternative proposals for having a more just society, short of the utopian proposal of taking an imagined jump to a perfectly just world.

This is nonsense. A transcendental approach seeks some a priori aspect of our cognition- in this case a sense of what is fair and just- and approves or rejects specific proposals on the basis of this intuition which, it posits, we all have as part of our 'hard wiring'- so to speak. We may deny that there are any transcendental truths but we can't deny that some people claim to have them. Though the thing may be arbitrary, it can and does exist. Some people feel that abortion is a crime just like cold blooded murder. They will hear no talk of mitigating circumstances or adverse social consequences. They refuse to believe us if we say 'there can be no such thing as a synthetic a priori judgment' because that is precisely what they claim to have. 

A perfectly just world would have no Judiciary or idea of Justice just as a world where everybody was always healthy would have no Doctors. This does not mean that there can't be people with a transcendental view of Justice or the duties of a Medical Practitioner in this imperfect world of ours. 

Indeed, the answers that a transcendental approach to justice gives – or can give – are quite distinct and distant from the type of concerns that engage people in discussions on justice and injustice in the world (for example, iniquities of hunger,

It is perfectly possible to have a transcendental belief that it is wrong to 'eat alone' when others are going hungry. Indeed, this is what the Rg Veda says. The fact is, most Religions consider Revealed Truths to embody transcendental judgments which motivate the devout to mitigate social evils  of the sort Sen lists

poverty, illiteracy, torture, racism, female subjugation, arbitrary incarceration or medical exclusion as social features that need remedying).
the distance between the transcendental and the comparative

There is no such distance. Transcendental just means an intuition we have as part of our hard-wiring. Indeed, Sen himself is a transcendentalist because he believes being a better man means being better at helping others selflessly. This is his intuition (unless he is virtue signaling) and it enables him to compare situations- e.g one where he gives money to a beggar so both he and the beggar can eat and the alternative which is that he gorges on food in an expensive restaurant while the beggar starves to death.  

Nevertheless, important as this elementary contrast is, the formal remoteness of the transcendental approach from functional judgements about justice does not in itself indicate that the transcendental approach cannot be the right approach. There might well be some less obvious connection, some relationship between the transcendental and the comparative that could make the transcendental approach the right way of proceeding to comparative assessments.

Either you have intuitions of a transcendental type or you don't. If you do, you make comparative assessments on that basis. If you don't, you would only do so because you were paid to do so or gained reputationally or in some other way. 

Suppose I have an intuition that woman over there is my soul-mate. This motivates me to propose marriage to her. But absent any such intuition, what is my motivation? It may be that what I feel is mere sensual attraction.  

That investigation must be undertaken, but the temptation to believe that any transcendental theory must carry within its body some justificatory grounds that would also help to resolve all comparative issues is not well founded.

Because nothing that is not justiciable and protocol bound requires 'justificatory grounds'.  

As it happens, some transcendental theorists not only concede that there is a gap here, but do so proudly enough, asserting the folly of going into the comparative sidetrack (and it is indeed a sidetrack in the purely transcendental perspective).

At one time there was the hope that 'transcendental deductions' would be canonical or non-arbitrary. Sadly, it seems,  'naturality' isn't part of human nature.  Still we may speak of 'Natural Justice' if not 'Natural Religion'. 

Robert Nozick, for example, is content to demand that all libertarian rights be fulfilled (this is his transcendental picture), but dismisses the issue of trade-offs between failures in the fulfilment of different types of rights (he has little use for what he calls ‘utilitarianism of rights’).

This is fine if the obligation holder has an incentive to provide the remedy to a right's violation. This is like the folk theorem of repeated games. Nozick was moving in an evolutionary direction- in some ways similar to Ken Binmore- when he died.  

Similarly, it is not easy to see how the diagnosis of perfection in the frameworks of Hobbes, or Locke or Rousseau

there are no such diagnoses. It was obvious that a perfect society would be an Eden of abundance.  

would take us to decisive comparisons among imperfect alternatives. The story is more complex with Kant or Rawls, since their elaborate reasoning about the identification of the transcendental solution does offer clues to some – though not all – comparative issues as well. For example, Rawls’s formulation of the difference principle, a component of his second principle of justice, gives us ground enough to rank other alternatives in terms of the respective advantages of the worst off.

This may appear to be the case till you remember that what people are doing in the 'original position' is hedging against ending up at the bottom of the heap. But the solution is to back a collective insurance scheme with 'moral hazard' provision rather than stipulate that the welfare of the poorest be lexically preferenced. 

Everybody buys insurance against specific risks. But, because of 'moral hazard' compensation will never be to the full value. People need to avoid risky behavior. They should have some 'skin in the game'. 

And yet this cannot be said about the other part of Rawls’s second principle, in which different violations of fair equality of opportunity would have to be assessed by criteria on which Rawls does not give us anything like a definitive guidance.

He wasn't an economist. He didn't get that if there is a natural monopoly then any type of wage, price or service provision discrimination could be justified. His theory was 'anything goes'.  

The same can be said of the violations of liberties, which would negate the fulfilment of the first principle, since liberties are of different types (as Rawls himself discusses), and it is not at all clear how different violations of liberties would be comparatively assessed. There are different ways of doing this, and Rawls does not privilege any one way over others. Indeed, he says relatively little on this question altogether. And that is, of course, fine for Rawls’s purpose, since a transcendental identification does not demand that this further comparative issue be addressed. A transcendental theory need not be what was called, in the Introduction, a ‘conglomerate’ theory (resolving transcendental and comparative issues simultaneously),

yet, if there is a transcendental intuition then this is what must happen though the 'principle of harmonious construction' remains elusive. A theory may be very clumsy in application without ceasing to be a theory.  

and even though there is more articulation in Rawlsian reasoning about comparative questions than in many other transcendental theories, a big chasm still remains.

But Rawls theory was garbage. He hadn't heard that people could buy insurance policies.  

A conglomerate theory is not needed by Rawls for his principles of justice (identifying perfectly just institutions),

He does not identify any such institution. He says that people would want their institutions to promote a particular outcome. He was wrong. People prefer to buy insurance against specific risks rather than agree to prioritize the plight of the poorest- just in case they find themselves in that class. 

Suppose I go up to Jeff Bezos and say 'look, we're both vulnerable to being fucked to death by super-models. If it happens to me first, I leave you all my money in my will so you can hire bouncers to protect you. You do the same for me. Do we have a deal?' 

Bezos tells me to fuck off because he can easily hire bouncers and thus guard against the risk of being fucked to death by super-models. He may even suggest that I exaggerate the risk of any such thing happening to me. Sad. 

and he does not offer one. But does not a transcendental identification in itself tell us something about comparative issues, even when those issues are not explicitly confronted?

Yes. There is an intuition of a certain type and if it is truly 'transcendental' it won't be led astray by mere sense-data. Bezos is wrong to reject my kind offer. I genuinely am at high risk of being fucked to death by super-models.  

Are there not some analytical connections here? Are we being led astray by artificial separations that do not exist? These doubts demand serious investigation.

No. Rawls was stoooopid. If you run a risk of ending up poor- buy gilt edged securities and get insurance of various types. Don't agree to a stupid compact with impecunious nutters like me.  

There are two questions, in particular, to address. First, could it be the case that transcendental identification of the perfectly just social arrangement will automatically tell us how to rank the other alternatives as well?

Yes. If an angel says 'this is perfectly Just' or 'perfectly Beautiful' we get additional data, not otherwise available, about Justice or Beauty. There is a 'base case' from which we can move forward. It's like what would happen if an angel told us we were on the Pareto frontier.  

In particular, can the answers to transcendental queries also take us, indirectly, the idea of justice to comparative assessments of justice as a kind of ‘by-product’?

Yes. If we know all true predicates of one object we will know everything that is true of all objects. This is like Yoneda Lemma.  

In particular, could comparisons of ‘distance from transcendence’ at which the different societal arrangements stand be the basis of such comparative assessment?

Yes. Essentially, we would have information about the supremum of Stalnaker-Lewis closest possible worlds.

Suppose an angel tells us that Sen is the best Indian economist. We would immediately know with certainty that all Indian economists are utterly shit.  

Could the transcendental approach be ‘sufficient’ for yielding much more than what its formal content suggests?

Yes, if there is costless 'verification' or 'zero knowledge proof'  regarding the 'extension' of a set or class. 

Second, if there is a query about sufficiency here, there is also one about necessity. Could it be the case that the transcendental question (‘what is a just society?’) has to be answered first, as an essential requirement, for a cogent and well-founded theory of comparative justice, which would otherwise be foundationally disjunctive and frail?

Sure. Why not? A useful theory of comparative justice need answer no such questions. If it tells rich people or big corporations which are the best jurisdictions to transact different types of business then it more than pays for itself. But a useful theory may not be cogent or well-founded- in the opinion of shitheads.   

Is the transcendental approach, aimed at identifying a perfectly just state, necessary for comparative judgements of justice as well?

Yes, if it is based on comparisons made by parties to a Social Contract. That's what Rawls does. Sadly, he forgot that Insurance Companies exist and thus his work was worthless.  

Implicit beliefs in the sufficiency or the necessity (or both) of a transcendental approach for comparative assessment clearly have had a powerful role in the widespread conviction that the transcendental approach is crucial for the entire theory of justice.

Either there is a 'hard-wired' justice instinct, or there isn't. Sen assumes such a thing exists but he may be virtue signaling. If there is such an instinct, then the transcendental approach is fine because it is saying we all have the same intuition though this may have been dimmed in some of us because we have led bad lives. But this is like saying God dwells in your heart and speaks to you with the voice of conscience. Nothing wrong with that at all. Plenty of good people live like that and enrich all our lives.  

Without denying the practical relevance of, or intellectual interest in, comparative judgements, the transcendental approach has appeared to many theorists to be a central requirement of a well-grounded theory of justice.

As opposed to a useful theory of justice- viz. the thing is a service industry which should, as Hume said, focus on utility and reducing transaction costs, promoting 'high trust' networks, and finding Coasian solutions to torts involving externalities.  

The hypotheses of sufficiency and of necessity would, therefore, need closer examination to determine the substantive place of transcendental theories in the political philosophy of justice. is the transcendental approach sufficient? Does a transcendental approach produce, as a by-product, relational conclusions that are ready to be drawn out, so that transcendence may end up giving us a great deal more than its overt form articulates?

Yes. If we say 'the State must own the means of production' or 'Society must serve God in the manner laid down by Holy Scripture', then the entire pattern of Society changes and we look at everything from a different point of view. 

More moderately, if like the people of Ukraine, we are attacked by a ruthless enemy, we will want to put the entire economy on a war footing. Every action will be judged solely by its impact our national struggle.  

In particular, is the specification of an entirely just society sufficient to give us rankings of departures from justness in terms of comparative distances from perfection, so that a transcendental identification might inter alia entail comparative gradings as well? The distance-comparison approach, even though it has some apparent plausibility, does not actually work.

Neither does anything else in Social Choice theory.  

The difficulty lies in the fact that there are different features involved in identifying distance, related, among other distinctions, to different fields of departure, varying dimensionalities of transgressions, and diverse ways of weighing separate infractions.

But all of these difficulties also arise in my decision whether to fart just now or wait a bit and take a dump.  

The identification of transcendence does not yield any means of addressing these problems to arrive at a relational ranking of departures from transcendence.

That is irrelevant. Only the opportunity cost- i.e. the next best alternative- matters. We are not required to rank anything else when making a choice.  

For example, in a Rawlsian analysis of the just society, departures may occur in many different areas, including the breaching of liberty, which, furthermore, can involve diverse violations of distinctive liberties (many of which figure in Rawls’s capacious coverage of liberty and its priority).

So what? Either there is an incentive compatible remedy or there was no right under a vinculum juris.  

There can also be violations – again, possibly in disparate forms – of the demands of equity in the distribution of primary goods (there can be many different departures from the demands of the ‘difference principle’).

Equally, there may be an overlapping consensus. The plain fact is, Juries have been delivering good enough verdicts for centuries.  

There are many different ways of assessing the extent of each such discrepancy and of appraising the comparative remoteness of actual distributions from what the principles of full justice would demand.

But there are also many different ways of getting an overlapping consensus. Juristic processes are protocol bound and buck stopped. That is a feature, not a glitch.  

We have to consider, further, departures in procedural equality (such as infringements of fair equality of public opportunities or facilities) which figure within the domain of Rawlsian demands of justice (in the first part of second principle).

But equitable remedies can be provided. Lawyers and Judges have been doing this sort of stuff for thousands of years.  

To weigh these procedural departures against infelicities of emergent patterns of interpersonal distribution (for example, distributions of primary goods), which also figure in the Rawlsian system, would require distinct specification – possibly in axiomatic terms – of relative importance or significance (or ‘trade-offs’ as they are sometimes called in the somewhat crude vocabulary of multidimensional assessment).

Which is what happens when two parties to a suit settle the matter between them- perhaps with some assistance from an arbitrator.  

But these valuations, helpful as they would be, lie beyond the specific exercise of the identification of transcendence and are indeed the basic ingredients of a ‘comparative’ rather than a ‘transcendental’ approach to justice.

Our intuition of what is just may be transcendental. Two parties to a suit may disagree as to what that intuition should be, but they can have an overlapping consensus. The thing happens all the time. In some cases one party may say 'well, I still feel, as a matter of principle, that I was in the right. But, it is expedient that I settle this matter'. But Justice is still served even if, at the end of the day, nobody is particularly happy. What matters is that the alternative- viz. disengaging completely- is demonstrably worse.  

The characterization of spotless justice, even if such a characterization were to emerge clearly, would not entail any delineation whatever of how diverse departures from spotlessness would be compared and ranked.

Which doesn't matter at all. I want to wear spotless underwear. I am not concerned with whether a pair of boxers worn by Trump has more horrible skid-marks than one worn by Biden. I just want clean underwear is all. Indeed, I'd rather got 'Commando' than wear anybody's dirty undies.  

The absence of such comparative implications is not, of course, an embarrassment for a transcendental theory itself, seen as a free-standing achievement. The relational silence is not, in any sense, an ‘internal’ difficulty; indeed, some pure transcendentalists would be utterly opposed even to flirting with gradings and comparative assessments, and may quite plausibly shun relational conclusions altogether. They may point in particular to their understanding that a ‘right’ social arrangement must not, in any way, be understood as a ‘best’ social arrangement, which could open the door to what is sometimes seen as the intellectually slippery world of graded evaluations in the form of ‘better’ or ‘worse’ (linked with the relationally superlative ‘best’).

This is why Social Choice theory is useless when it comes to a Theory of Justice. Judgments aren't choices. They only arise where an issue is justiciable and they must be more or less protocol bound and buck stopped. Public Policy is one kettle of fish. Jurisprudence is another. Sen is wrong to confuse the two.  

The absoluteness of the transcendental ‘right’ – against the relativities of the ‘better’ and the ‘best’ – may or may not have a powerfully reasoned standing of its own (I refrain from going into that issue here).* But it does not, of course, help at all – and that is the central point here – in comparative assessments of justice and therefore in the choice between alternative policies.

Justice is not about choosing policies. It is about whether those policies are implemented in a manner the law considers just and fair. 

It would be foolish to blame the Chief Justice if the Chancellor of the Exchequer screws up the Nation's finances. 

I suppose what Sen is getting at is the claim by some politicians to be able to deliver 'Social Justice'. But this is merely a figure of speech. The meaning is 'we will take from the rich and give to the poor- if you vote for us'. That comes under the heading of fiscal policy. In practice, if the rich can flee the jurisdiction, the tax burden is shifted to poor but inelastic suppliers of factors of production while the lazy get paid a little money to vote for the ruling party.  

To be sure, members of any polity can imagine how a gigantic and totally comprehensive reorganization might be brought about, moving them at one go to the ideal of a fully just society. A no-nonsense transcendental theory can serve, in this sense, as something like the grand revolutionary’s ‘one-shot handbook’. But that marvellously radical handbook would not be much invoked in the actual debates on justice in which we are ever engaged.

Why not? In California there is talk of massive reparation payments to African Americans. This could be extended in all sorts of directions- e.g. White folk must give up their seats on buses to African Americans.  

Questions on how to reduce the manifold injustices that characterize the world tend to define the domain of application of the analysis of justice;

why restrict that domain? Why not promise voters millions of dollars and then laugh at them once you are in office?  

the jump to transcendental perfection does not belong there.

Yes it does if that is what gets you votes.  

It is also worth noting here the general analytical point, already noted in the Introduction, that the diagnosis of injustice does not demand a unique identification of ‘the just society’,

it is merely an arbitrary assertion. How is it just that I've got a tiny dick or that everybody thinks I'm a flatulent fool when, deep in my heart, I know myself to be wise and sagacious?  

since a univocal diagnosis of the deficiency of a society with, say, large-scale hunger, or widespread illiteracy, or rampant medical neglect,

this is an economic deficiency. The Society itself may be very just. Everybody has an equal chance of dying a miserable death.  

can go with very different identifications of perfectly just social arrangements in other respects.

No. If an arrangement can be properly identified as being 'perfectly' x or y, then 'unicity' is established. Furthermore there is a category with a 'natural transformation' of a certain type. A lot of extra information has been given to us for free. Indeed, it is possible that all information has been given to us. (because we don't know whether zero-knowledge proofs are possible in such cases). 

Even if we think of transcendence not in the gradeless terms of ‘right’ social arrangements, but in the graded terms of the ‘best’ social arrangements,

it makes no difference. There is unicity. Extra information has become magically available.  

the identification of the best does not, in itself, tell us much about the full grading, such as how to compare two non-best alternatives

we don't need to compare them anymore than we have to decide whether to wear Trump's underpants or Biden's.  

, nor does it specify a unique ranking with respect to which the best stands at the pinnacle;

but extra information has become available such that all rankings will change. But we are only concerned with the supremum. Those other rankings may or may not converge because the information set re. the 'intension' has changed. 

indeed, the same best may go with a great many different rankings at the same pinnacle. To consider an analogy used earlier, the fact that a person regards the Mona Lisa as the best picture in the world does not reveal how she would rank a Picasso against a Van Gogh.

It may do so, statistically. A Google search may reveal that people who like Da Vinci also like Van Gogh but are lukewarm about Picasso. Somebody may have written a paper on the link between genius and madness. Da Vinci had the first. Van Gogh, poor fellow, went insane.  

The search for transcendental justice can be an engaging intellectual exercise in itself, but – irrespective of whether we think of transcendence in terms of the gradeless ‘right’ or in the framework of the graded ‘best’ – it does not tell us much about the comparative merits of different societal arrangements.

By contrast, Social Choice theory tells us nothing at all. This raises the question, how do we judge comparative merits of different societies? One answer is that we look at entry and exit. Other things being equal, are smart people moving from one place to the other? If so, chances are their societal arrangements are better in some important respect. 

Is the transcendental approach necessary?

Yes, if you are saying there is a hard-wired 'justice instinct' or intuition of a particular type- e.g. one which thinks it unfair that Bezos, who has done useful stuff, is rich while I am poor because I'm utterly useless. 

Sen seems to have this belief but won't specify the world he'd like to see. He just gasses on about hunger and the subjugation of women and so forth. The trouble is, stuff like this may be happening in war-torn areas or places where nice Westerners get kidnapped and beheaded. So he isn't really saying anything substantive at all. It's just a case of 'Boo to poverty! Malnutrition sucks ass bad time!'  

Consider now the hypothesis that the identification of the best, or the right, is necessary, even if not sufficient, to rank any two alternatives in terms of justice.

This is not a hypothesis. It is a tautology. If you say one of two alternatives is 'right' then you have ranked them in terms of justice. This is a sufficient, but not a necessary, condition.  You may say nothing and silence may be taken for consent. Alternatively, if you say some other situation is 'right', then some legal or factual aspect of that case applies to one but not the other of the alternatives. Judgment should be given accordingly. This too is a sufficient, not a necessary condition. There may be no 'stare decisis' case with applies to the present situation. 

In the usual sense of necessity, this would be a somewhat odd possibility.

It is nonsense, anyway you look at it.  

In the discipline of comparative judgements in any field, relative assessment of two alternatives tends in general to be a matter between them, without there being the necessity to beseech the help of a third – ‘irrelevant’ – alternative.

Unless the third is known to have some maximal property and thus can provide extra information or guidance. 

Thus, suppose we have to choose between two mathematicians for an important assignment. We are told that Terence Tao is the best for the job but he is unavailable. We would then chose the mathematician who is closest to Tao in his approach and fecundity .  

Indeed, it is not at all obvious why in making the judgement that some social arrangement X is better than an alternative arrangement Y, we have to invoke the identification that some quite different alternative, say Z, is the very ‘best’ (or absolutely ‘right’) social arrangement.

It is extra information of a relevant type. I argue passionately for Van Gogh over Picasso. You are initially impressed. Then I reveal my favorite painting features dogs playing poker. You would now be inclined to back Picasso because of 'cognitive dissonance'.  

In arguing for a Van Gogh over a Picasso we do not need to get steamed up about identifying the most perfect picture in the world, which would beat the Van Goghs and the Picassos and all other paintings in the world. It might, however, be thought that the analogy with aesthetics is problematic since a person might not even have any idea of a perfect picture,

but if it is dogs playing poker we can draw the inference that the guy is a philistine.  

in a way that the idea of ‘the just society’ has appeared to many to be clearly identifiable, within transcendental theories of justice.

but if this involves raping and beheading kuffars we can draw the inference that the guy isn't a Rabbi.  

(I will argue presently that the existence of a best – or inviolate – alternative is actually not guaranteed even by as complete a ranking of relative achievements of justice as possible, but I proceed, for the moment, on the presumption that such an identification can be made.

By arbitrary stipulation- sure.  It may be a fact of the world that some people have 'transcendental' intuitions about Justice. This is an uncorrelated asymmetry with an associated 'bourgeois strategy'. We are welcome to evaluate that strategy and see if it might be something we want implemented. Alternatively, if guys with that intuition are becoming the majority, we might want to run the fuck away while we can still safely do so.

Ideas and intuitions of Justice do matter. They can lead to big changes in a Society. It is right that we take an intelligent interest in the direction in which jurisprudence is going in our country. However, Sen-tentious  Social Choice Theory won't be of any help in this matter. It can't show us a single complete preference ordering for any person, let alone a society. It demands too much information and cognitive power but even then can't reach any useful type of conclusion. 

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