In an article on Sen's memoir, Partha Dasgupta writes-
In a series of strikingly original papers in the late 1960s, culminating in his magisterial Collective Choice and Social Welfare (1970), Sen applied a system of reasoning initiated and developed in a great masterpiece of twentieth century thought, Kenneth Arrow’s 1951 Social Choice and Individual Values, and began the construction of the normative grammar essential for understanding ideas of social wellbeing.
Social wellbeing was already well understood. Post-War Europe had created welfare states. 'Normative grammar' had to do with things like Governments building houses and hospitals and schools and Universities and 'pump-priming' the economy so that unemployment was kept down and competitive pressure drove wages upwards in a manner that led to the deployment of new technology. Neither Sen nor Arrow contributed anything to this with their stupid theorems.
Sen’s book is technical (it relies on the logic of relations deployed by Arrow)
Who got it from Tarski. The problem is that preferences are intensional and epistemic. They aren't even anti-reflexive- i.e. equal to themselves. Thus they can't be subjected to a 'calculus of relations'.
but is graced with a literary text that explores in pithy prose the analytical foundations of classical utilitarianism among other ethical theories.
Those foundations are shit. Utility can't be measured. It is 'intensional' and changes when the knowledge base changes. It is also 'impredicative'. True, we can focus just on money and imputed income of various sorts. But, that is useful. Utilitarian theorists pride themselves on being utterly useless.
Arrow’s book introduced the idea that democratic voting rules (e.g. rules governing parliamentary elections in the UK) should not be installed without being screened for whether they embody democratic values.
Not even Arrow was that stupid. He understood that a functioning democracy changed its voting rules from time to time according to its own laws and subject to its own written or unwritten constitution.
A typical voting rule in the West requires voters to register only their most preferred candidate among those on the ballot. For example, in the rules governing election to UK’s parliament— ‘frstpast-the-post’ in common parlance—the candidate receiving the highest percentage of votes is declared winner even if the vote falls short of the 50% threshold. Arrow noted that such a system ignores voters’ preferences over their less-favoured candidates and took it to be obvious that voters should be required to rank all candidates on the ballot.
The cretin didn't get that, in a democracy, voters can't be made subject to the whims and fancies of pointy headed pedants.
That may seem a tiresome, technical requirement, but it matters hugely, because among other shortcomings, the first-past-the-post system allows, even encourages, ‘spoiler candidates’ to undermine democracy.
No it doesn't. You can always spoil a spoiler by running more and more spoilers till they all lose their deposits.
To see how, imagine that in an election in which there are three candidates, x, y, z, 47% of the electorate vote for x, 48% vote for y, and 5% vote for z. Under the frst-past-the-post rule, y would be declared the winner. But suppose each of the 5% of voters supporting z, had they been asked, would have declared a preference for candidate x over candidate y (because, say, candidate z espouses an extreme form of policies espoused by x and is thus even farther from y in his political views). That preference would not of course be registered under the prevailing election rule, but as 52% of the electorate favour candidate x over candidate y, the rule can scarcely be called democratic.
Why not? Britain is democratic. It has this system. It also does have a third party which sometimes forms a coalition with one or other of the main parties. The third party wants proportional representation. But they keep fucking up and so they won't get it. Some countries have two round elections for the head of state as do some political parties. But these are mere details. Voting rules don't matter. What matters is if there is a good enough political culture and general social cohesiveness.
Candidate z spoils the democratic mandate of x by taking advantage of a defective electoral system and hands over the election, perhaps unwittingly or perhaps owing to hubris, to candidate y.
That is merely a manner of speaking. It is x's own fault if he couldn't communicate clearly enough that z was a spoiler. Alternatively, his party should have run an equal and opposite spoiler of their own. Showing a good sense of strategy by winning an election signals tactical brilliance of a sort useful to the country.
(Instances of spoiler candidates overturning democracy would appear to have occurred in recent years in Presidential elections in the USA and France.)
Not really. In each case, the guy whining about spoilers soon shows some big character flaw while winners reveal there was more to them than met the eye.
Arrow proposed instead a set of axioms that are widely thought to be democratic
they were crazy
and are based only on voters’ rankings over the candidates on ballot and asked whether there is a voting rule satisfying them that yields an election result no matter what voters’ rankings over the candidates happen to be. His remarkable fnding was that there is none.
Because his 'axioms' were stupid.
In the process of narrowing down the list of voting rules by requiring them to satisfy democratic values while ensuring that the rules are applied only to voters’ rankings over the candidates on ballot, he found that there was none left! In fact, the bare bones of Arrow’s ‘Impossibility Theorem’ had been discussed by the eighteenth century thinker, the Marquis de Condorcet, in his dissection of majority rule. Condorcet asked us to consider three voters, numbered 1, 2 3, who are to vote on three candidates, x, y, z.
Because that's how elections work- right? 1.4 billion Indian voters vote for 1.4 billion candidates.
Majority rule declares a candidate to be the winner if and only if she beats all others in head-to-head contests.
No. Majority rule obtains if the majority of people shrug their shoulders and agree that the outcome represented the will of the people. It doesn't matter how that outcome was arrived at. I may allege that Rishi Sunak got to be PM because he personally sucked off 33 million British people. I don't stoop to that sort of thing myself which is why I'm not living in Number 10. Still, I have to admit that Dishy Rishi is the democratically elected Prime Minister of the country even though no voter in 2019 thought he'd get the top job.
Imagine now that voter 1 ranks candidate x over candidate y and candidate y over candidate z; that voter 2 ranks candidate y over candidate z and candidate z over candidate x; and that voter 3 ranks candidate z over candidate x and candidate x over candidate y. He noted that in such a case x beats y in a head-to-head contest because two voters, 1 and 3 (a majority) rank x over y; that y beats z in a head-to-head contest because two voters, 1 and 2 (who also form a majority) rank y over z. As x beats y and y beats z, we may think that x beats z, but we would be wrong, because two voters, 2 and 3 (yet another majority) —rank z over x, meaning that candidate z beats candidate x in a head-to-head contest. We have a contradiction, for we are left with a cycle: x beats y, who beats z, who beats x, who beats y, … ad infnitum.
So what? X wins under first past the post. Z may blame Y for being a spoiler- but that's life.
Arrow considered voting rules for situations where the number of candidates can exceed three and showed that such cycles as those that Condorcet unearthed arise in all democratic voting rules when voters’ preferences over a triplet of candidates are markedly non-aligned.
This doesn't matter in the slightest because Preferences are 'intensional'. They have no calculus. If even anti-reflexivity is off the table, how do you expect to get transitivity?
One may take Arrow’s finding to be saying that democracy works only when citizens share something like a common ethical culture.
Fuck off! It is obvious that those who think Arrow's theorem aint ignorant shit share a common ethical culture- a shit one. Yet they may be citizens of democracies with very different cultures and voting rules.
In a 1966 paper “A Possibility Theorem on Majority Rule”
which assumes everybody has a weak preference ordering over all alternatives. This means reflexivity and connectedness are assumed. But, one alternative can be termed the one everybody with hindsight would regard as the best feasible outcome. We don't know what that alternative is but we can't prove it doesn't exist. By connectedness, it must be an available alternative. Now if it were known which alternative it actually was then that alternative would become more attractive. This is like 'Newcombe's problem'. If an angel descended from on high and said 'there is an alternative which best solves Society's coordination problem or which will prove providential with hindsight' our preferences would change. This defeats reflexivity for at least one alternative. The thing would be more preferable than itself if its true identity were known. We understand the intension 'best alternative for Society with hindsight' but its extension is not known. This makes nonsense of the calculus of relations. Liebniz's law ceases to apply.
Sen identified a formal way of articulating what a common ethical culture means for majority rule to work well.
It involves 'value restriction'. But this is arbitrary.
To illustrate, suppose voter 1 in Condorcet’s example ranks (candidate) x over y and y over z; voter 2 ranks x over z and z over y; and voter 3 ranks z over y and y over x. The rankings do not clash in the way they do in the Condorcet example. It is easy to see that in this situation majority rule would declare x the winner because x beats both y and z in head-to-head contests.
Why bother with voting? Let's just value restrict votes and get the result we want.
In a 2008 paper “On the Robustness of Majority Rule”, Journal of the European Economic Association, Eric Maskin and I showed that if the number of voters is large, the restrictions on their rankings over candidates under which majority rule yields a winner are fewer than the restrictions demanded by any other voting rule satisfying Arrow’s axioms on democratic values. That is the sense in which majority rule could be said to be the most robust among all democratic voting rules.
It is nonsense. First past the post yields a winner as does having run-offs and a final clash between two candidates. But both are arbitrary and will display hysteresis. But this doesn't matter if people shrug their shoulders and say 'the people have spoken'. The winner is unambiguous.
Arrow’s theorem is central to any understanding of the idea of democracy
Fuck off! A democracy is any regime where the administration changes from time to time in accordance with the will of the people. Suppose, some group objects to a given change then there is secession or civil war. Only if when the objection ceases to hold and there is consensus that the people have put such and such administration in power can we say that Democracy prevails.
A Democracy may change its voting rules or method of representation without ceasing to be a democracy. What matters is if there is a consensus, however grudging, that the people chose the administration.
Arrow's theorem was simply an expression of stupidity and bad mathematical practice.
and was in due course regarded by political scientists to be so.
Not actual practicing political scientists- i.e. the sort of guys paid big bucks by political parties to help them win elections- but stupid pedants teaching worthless shit.
But as voting rules were not on the agenda of mainstream economics, it remained a curiosity by the profession for some two decades. It should not have been a curiosity because ‘political candidates’ represent the ‘economic policies’ they advocate, and economic policies give rise to consequences, for example, the allocation of resources, which are the central objects of interest to economists.
The median voter theorem of Duncan Black predates Arrow and has been revived by Dasgupta & Maskin. We can trace it back to Hotelling. But practical politicians knew all about it and about 'Shapley values' and so forth long before mathematicians spelled them out.
Voting rules for choosing among political candidates are meant for deployment at the polling station. Ideally citizens would vote in line with their ‘social preferences’ (the economist John Harsanyi — “Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility”, Journal of Political Economy, 1955—would have used the term ‘ethical preferences’), not their personal interest, advice my fellow students and I were given in the civics lectures I attended at my school in Varanasi, where our teacher insisted that citizens need an ethical language in which to decide how to vote in national and local elections.
I suppose teachers in Varanasi are now telling kids to vote for Modi for this reason. Back then it would have been for Uncle Nehru. But the teacher was wrong. We know our own preferences. That's what we should reveal in our votes. 'Ethical' or 'Social' preferences are likely to exhibit 'preference falsification' and fallacious reasoning.
Arrow chose the title ‘Social Choice and Individual Values’ for his book, his intention was to draw a distinction between voting rules and the directives that should guide the citizen on whom to (more accurately, what to) vote for.
Why have votes if you are also going to have directives? Vote for the guy whom you think will make you personally better off. Let others do the same. This way you get information aggregation not a 'Keynesian Beauty contest' where people are voting for who they think other people will vote for. That way you end up with Miss Piggy getting elected instead of somebody cute whom you'd actually want to pork.
Ethical considerations that are directed at identifying voting rules are thus different from the ones citizens will wish to entertain for arriving at their social preferences over alternative policies.
They are irrelevant. Stick with what works or what legislators have amended after due consideration. What matters is whether there will be consensus after the election that the people have spoken and got the government they want- or can live with.
Arrow rightly disallowed intensity of voters’ preferences over the candidates on ballot because otherwise voters would be tempted to inflate their feelings about them.
Give them a 'budget' so they have to economize, not inflate. Arrow said in his paper that people vote with money in markets.
The riots outside polling stations in non-orderly countries we occasionally read about are expressions of that.
No. They arise because of 'booth capturing' by gangster politicians. There can be riots or even an insurrection after an election. Only when this has settled down can we say Democracy is functioning.
For a citizen to discover her social preferences over, say, economic states of affair requires a different kind of ethical reasoning.
Fuck off! She needs to work out which candidate is likely to improve her economic condition. She needs to display her true preference rather than do what she thinks God would approve of.
She will, for example, want to be able to compare people’s needs, which means interpersonal comparisons of individual well-beings would be an essential feature in her exercise.
She does this already. She sees a lady like herself with more money and decides that lady has higher utility. She votes for the guy who says he will help her get more money. On the other hand, maybe she compares herself with a woman who keeps getting raped. She decides being raped aint fun. She votes for the guy who is tough on crime.
We may imagine that in order for a citizen to discover her social preferences, she places herself successively in everyone’s shoes, as it were, to get an understanding of their interests; for as Atticus Finch in To Kill a Mockingbird famously advised his daughter Scout, “You never really understand a person until you consider things from his point of view – until you climb into his skin and walk around it”.
This is a fucking waste of time more particularly in a big country like India with 1.4 billion people. The voter has information not available to anybody else- viz. which candidate would make them personally better off. Let them reveal that information.
The point of the thought experiment is that it would not only enable the citizen to construct everyone’s well-being functions but also to have an inbuilt mechanism for comparing them.
Why stop there? It would also enable the citizen to experience a mental simulation of anal sex with every other citizen. Furthermore, in a big country like India, you would also learn 780 languages as well as nuclear physics and medicine and how to write utter bollocks like Dasgupta.
She would then use that information to construct every individual’s well-being as a function of the various possible states of affairs.
Like how many orgasms she will experience if she has affairs with one billion of her fellow citizens.
Her next step would be to aggregate the individual well-being functions she has constructed. We call the aggregate her ‘social well-being function’ and the ranking of states of affair that corresponds to it her ‘social preferences.
No we don't. Her social preferences are the ones in which she is best off. Her knowing the minds of everybody else doesn't matter in the slightest because she remains confined to her own body.
’ Thus far, there is nothing novel in the thought experiment.
It is stupid shit.
Indeed, it had been routinely deployed by moral philosophers.
No. Mystics may speak of 'tuirgen' or a knight's tour of all possible sentience- but this includes knowing what it is like to be a fish or a bird or a Spaghetti monster in the Andromeda galaxy.
What was novel about Sen’s work is that he uncovered the assumptions regarding the measurement of personal well-being functions and the nature of interpersonal comparisons in each of several well-known moral theories.
He wrote stupid shit just as Dasgupta is writing stupid shit.
Consider, for example, the broad class of utilitarian theories in which the social well-being function is the sum of the individual well-being functions.
For which money and imputed income from owner occupation etc. is a good enough proxy. This relates to the tax base and is measured by National Income accounts.
Sen’s point was that, as with temperature, well-being does not come in an absolute scale, and that utilitarianism requires individual well-beings to be measurable in scales that are related to one another in a positive linear fashion.
No. It is enough if they are measurable.
To illustrate, recall the rule for converting temperature in the Centigrade scale into the Fahrenheit scale, which is to multiply the temperature by 9/5 and to then add 32. The relationship between the two scales tells us that it is meaningless to claim, say, that today is twice as hot as it was yesterday (because even if it were true in one scale, it would not be true in any other scale);
Then it is true if one scale is prevalent or in official use. This is not a meaningless claim at all.
what would be meaningful would be to claim, say, that the diference between today’s temperature and yesterday’s temperature is four times the diference between yesterday’s temperature and the temperature the day before yesterday (because that statement is independent of the scale in which temperature is measured).
This is a 'scale independent' observation. But that doesn't make it more or less meaningful. We still need a scale to tell us whether it is cold or hot outside.
Likewise, Sen observed that if the citizen is a utilitarian, the individual well-being functions must not only be unique up to positive linear transformations (as is the case with temperature),
in other words a well being function is meaningless unless it has a scale. But it doesn't. Nobody has found one. Hence there are no utilitarians. Still, we can take money as a proxy for utility but that would be vulgar- right?
but also that the units in which individual well-beings are measured are fully comparable (otherwise summation would not be a valid aggregation of individual well-beings), though the levels need not be comparable.
Which is fine with money but can't be done with 'well-being' or 'utility' or 'capabilities'
To appreciate the meaning of this observation, consider a society of three people, including the citizen in question. Imagine that on using a particular scale of measurement the citizen discovers that the well-beings of the three individuals in state of afair s would be, respectively, 35, 20, 45, and in state of afair s* they would be, respectively, 30, 25, 40. Choice of the scale is an expression of a value judgement on the part of the citizen and, as a utilitarian, she concludes that s is more commendable than s* because (35+20+45) exceeds (30+25+40). Notice that her conclusion would be the same if she were to use a measurement scale that was a multiple of the scale she used originally, say fve times. That is because 5(35+20+45) exceeds 5(30+25+40). Note also that her conclusion would remain the same if she added or subtracted constant numbers to either scale, say a, b, and c. That is because 5(35+a+20+b+45+c) exceeds 5(30+a+25+b+40+c) no matter what numbers a, b, and c happen to be (for they cancel one another in the comparison). However, the citizen must be consistent when she moves from one scale of measurement to another, as she does in the above example. If she multiplies someone’s well-being by 5 (as in the example), she must also multiply the wellbeing of all the others by 5; otherwise, she would not be using the same scales of measurement. To confrm, imagine that she multiplied the well-being of persons 1 and 3 by 5, but multiplied the well-being of person 2 by 10. Now state of afair s* would appear superior to state of afair s, because 5(35+20+45), which is 500, is less than (5 × 35 + 10 × 25 + 5 × 40), which is 625. It would be as though she was to claim that an object whose temperature is 100° in the Fahrenheit scale is hotter than an object whose temperature is 45° in the Centigrade scale. That is the sense in which, as Sen noted, utilitarianism requires unit comparability of the individual’s well-being (the multiplicative factor must be the same), but not level comparability (the additive factor need not be the same).
What a useless thing to point out! The fact is nobody has found a scale for well-being. Why get worked up about people carelessly confusing one imaginary scale with another which is equally non-existent?
Throughout this analysis, Sen applied Arrow’s technical machinery
which is vitiated by the intensional fallacy. There are no sets or unique pre-orders because preferences are not well defined and are impredicative or epistemic in character. Thus thy don't obey Liebniz's law of identity.
to explore social preferences that reflect not just utilitarianism but broader normative systems, including those that invoke the language of rights.
Which are Hohfeldian incidents. But Sen didn't know this.
His book, an instant classic, brought the foundations of welfare economics into mainstream economic reasoning.
No. Social Choice became a ghetto for nutters. The mainstream focussed on doing stuff that was useful to Governments or Corporations.
Sen’s principal accomplishment was to show what must be assumed in relation to the measurability and interpersonal comparability of individual well-being for an ethical system to be coherent.
No. He showed he was a stupid blathershite who didn't give a toss that his own people were being slaughtered by the Pakistani army before dying of starvation in democratic Bangladesh. An ethical system must first be ethical. Mathsy masturbation is not ethical more particularly if you pretend that something whose extension is not known is actually a set.
The reverse problem, of determining the implications of sets of ethical values on the structure of ethical thought,
Ethical values supply the structure of ethical thought. Ahimsa is the foundation of dharmic ethics. But there is no 'set of ethical values' because ethical values are intensional.
which is the counterpart of Arrow’s question regarding voting rules, is harder.
The counterpart of Arrow's theorem is Kuhn's no neutral algorithm.
The idea is to determine the structure of the social well-being function from assumptions about well-being measurement (e.g., that well-beings are unique up to positive linear transformations, as in the above example)
if so why hasn't anyone come up with a scale for well-being? Why not determine the structure of a stable for unicorns by assuming unicorns are one dimensional?
, about the extent to which interpersonal comparisons of well-being can be made, and from such value judgements as that individual well-being should enter the sought for measure of social well-being in a symmetric way.
why not add a value judgment that a one dimensional unicorn should symmetrically exit that measure and bring us a pepperoni pizza?
In a remarkable pair of articles Claude d’Aspremont and Louis Gevers (“Equity and the Informational Basis of Collective Choice”, Review of Economic Studies, 1977) and Eric Maskin (“A Theorem on Utilitarianism”, Review of Economic Studies, 1980) presented ethical axioms which direct the citizen to sum individual well-being functions for discovering her social preferences.
Even though she already has social preferences because she has a body and that body would be better off under certain social conditions rather than others. We might want a Benthamite sage to do sums and publish the result but we'd still all be better off voting our true preferences because that's what information aggregation is all about.
Their papers, and several elaborations by others, took Sen’s work as their starting point and placed the axiomatic formulation of judgements on social well-being in parallel with the axiomatic formulation of voting rules.
They were a waste of time. Voting rules can generate stability or instability but what really matters is whether there is broad acceptance that the outcome of elections represent 'the will of the people'. If this is absent there may be Civil War or a disintermediation of organs of the State.
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