Amartya Sen's Nobel Prize was for two very different things- one was his theory of famines which was wholly and mischievously wrong and the other was his well publicised belief that 'Democratic commitment' and 'Public Reason' have been greatly advanced by a theorem which either assumes P=NP (i.e. is ignorant) or else is based on a stupid and barefaced lie.
This theorem (Arrow's Impossibility result) implies that if everyone prefers to have a deterministic Vote aggregating system which everybody agrees delivers results that are the 'best' in some objective, value-free, sense, though they may not be able to at all 'quickly' work out all the steps by which the result was arrived at, (i.e. there is only NP solvability) then, if this system were implemented, it wouldn't be Democratic at all. What we would actually have is a Dictatorship!
This theorem is easy to prove iff we define 'Dictator' as a guy who wants and knows what is best for Society- perhaps by some non deterministic procedure, or superior Ethical intuition or 'Divine' inspiration- and therefore makes the same choices as the ideal Bergsonian SWF or Perfect Voting rule. Clearly, the theorem is now a tautology- it poses no scandal unless we think P=NP in which case it is a puzzle as to why a deterministic SWF can't get the same result as a possible voter able to use non-deterministic methods. If, as is likely, P is not equal to NP, there is no scandal- just a tautology of a misleading and disingenuous kind.
Still, one can't deny, this is a very wonderful theorem because it can be also be used to prove the impossibility of my neighbour 's cat iff we define the tabby in question as an Arrowvian method of aggregating preferences which must satisfy certain 'seemingly reasonable' conditions specifically chosen so that the thing is impossible because one of the conditions is not reasonable at all but rather is utterly mad. Of course, we could achieve the same end just by lying. But where's the fun in that?
Sen's greatness lies in his deployment of certain bien pensant caveats which suggests that considerations of Social Welfare exceed economics and involve philosophical issues which may cash out as value judgements, or Samuelson type 'ethics', but not yet, never yet. Instead we should indulge in a type of 'Deliberative Democracy' which never decides anything, preferring instead to just go on repeating platitudes couched in specious arguments and supported by bare-faced lies.
However, if philosophical issues really have salience- i.e. if some process of Public Reason can change Preferences, or motivate meta-preferences, in a manner such that, under ideal- perhaps Rawlsian- conditions, everybody would want the same outcome for Society- then, there could be a Platonic Guardian or Benthamite Oracle or Newcombe Predictor who arrived at the same conclusion independently.
Since, by definition, such a person would be stigmatised as a Dictator if included in the voting process- and Arrow doesn't allow us to exclude such a person- Arrowian Non-Dictatorship would not be a desirable property for a Collective Choice mechanism to boast. Why? Because it specifically bars the sort of outcome which would make it otherwise desirable.
Had Sen simply said 'Arrow's SWF is not at all isomorphic to a Bergson-Samuelson type SWF and proves nothing except that if you define something which aint Dictatorial as Dictatorial all you have done is utter a stupid lie' then he wouldn't have gotten to an Academic position where he could tell stupid lies about the true cause of the Bengali famine without being laughed at in Oxford or spat upon in Calcutta.
Perhaps Sen couldn't, in good conscience, say any such thing. Maybe, he genuinely thinks Arrow's result implies something very important about the nature of Democracy- viz. that it is shite and so we should all continually talk shite coz that's Democratic and Civilised people are democratic so just get with the program and start talking shite immediately you great big Bengollywog you. Don't let the side down. The World is watching.
He wrote-
The informational foundation of modern social choice theory relates to the basic democratic conviction that social judgements and public decisions must depend, in some transparent way, on individual preferences, broadly understood.
Nope. To reduce vulnerability to predators and parasites, human beings should always try to baffle any preference revelation mechanism. Indeed, not knowing one's own preferences is a safer strategy- which is why Evolution has ensured that there is no Momus window into the heart even for one's own ego.
Similarly, it is better to have Social Judgements which are robust to moment to moment changes in preferences so that the Regulatory or Normative environment is predictable and reduces Uncertainty in formulating long term plans.
Since, Newcombe type problems have salience in many Social and Economic processes, Preference falsification shouldn't be cognitively dissonant- and, indeed, the evidence is, it isn't. Pedagogues who write books are constantly astonished that people are inconsistent. They may support Liberty for themselves but not for others whom they exploit. Such pedagogues attribute causality to soi disant Great Men who wrote some pamphlet long ago descrying this inconsistency. However, such people were dismissed as antagonomic cranks who were either guillotined or condemned to the Bastille of Pedagogy or whose heads were lost to the community by some self-selective process of impressment into the condition of being the galley slave of a Scholarship long since run aground.
Nobody does not know, it is cognitively costly to have rational, or even alethic, preferences over all Social options though 'self deception' in this respect is an Evolutionarily Stable Strategy. Indeed, for analogous reasons, regret minimisation would militate for big saltations or discontinuities in Preference profiles. Meta-preferences should link to Tardean mimetic rules of a certain sort so that there is canalistion and capacitance diversity.
Ultimately, we have to recognise Preferences are just metaphysical tosh- like Utility functions. Social judgements shouldn't be based on them. Rather, there are canons specific to Judgement that collective Jurisprudence too should adhere to. The same point may be made about Public Decisions. To make them dependent on individual preferences is stupid. Rather they should conform to the canons specific to Public Administration. This is not to say that Information aggregation isn't important. It is, but more important yet is that Public Decisions are free of ambiguity, Agenda control problems, race hazard or concurrency problems and so forth.
Arrow's resurrection of Condorcet in the early Fifties has a certain Historical and Cultural significance. No doubt, back then, there was some point to pretending that mathematical logic could serve an ideological purpose. After all, at that time, Command Economies were spreading faster than Market economies. In the Sixties, following China's humiliating defeat of India, more and more ex-Colonies were choosing to go down the 'One-Party' path.
Those days are long gone. The Berlin Wall fell before Sen got his Nobel. But the Hayekian writing on the wall was clear to see by the beginning of the Eighties- i.e. the last time Arrowvian Social Choice Theory had a pulse. Since then, Chichilnisky and Saari have given us a notion of 'topological dictators' where utility functions are continuous. but the interpretation of the notion has nothing to do with 'Dictatorship' as opposed to Banzhaf Coleman type voting power.
Currently, Democracy and the Rule of Law are sufficiently attractive in their own right. Mathematical logic can be excused the duty of telling stupid lies in this respect. Why? Rather than prove the existence of God, as in Godel, or the Hitler in the ballot box, as in Arrow, it has genuinely alethic, and therefore useful, things to do.
Sen doesn't. He is still saying shite like this- The emergence of this democratic instinct relates closely to the ideas and events that surrounded the European Enlightenment. Even though the pursuit of democratic social arrangements drew also on various earlier sources and inspirations, it received a definitive delineation and massive public acknowledgement only during the Enlightenment, particularly - but not exclusively - during the second half of the eighteenth century, which also saw the French Revolution and American independence...
No axiomatic structure yields the existence of a dictator 'as a joint implication of chosen axioms'. Arrow defined a possible voter who always agrees with the Bergsonian SWF as a dictator. He arbitrarily restricted the SWF to the class of deterministic functions but allowed profiles to be non-deterministically verifiable solutions to the SWF. Clearly there is a P/NP type problem here and if Social Choice theory hadn't died long ago this would be the focus of research. Arrow's method doesn't make any stipulation about the time class of solutions so it has no real world application. But for that same reason, we know it to be tautological nonsense featuring semantic dishonesty. His 'Dictator' arises from one of his axioms. It didn't arise from any combination of the others. It is independent, utterly arbitrary, and thus itself quintessentially 'Dictatorial'.
By Dictator, in ordinary English, we mean a guy who has power over others. What Arrow is describing could be a mute or accidental Oracle who has no power. Alternatively, his 'Dictator' could be a Judas Goat or even, as D.G.Saari suggested, a sort of social chameleon like Woody Allen in Zelig.
If there is a Dictator in the common acceptation of the word, it would be a foolish waste of time to aggregate preferences or stipulate for 'independence of irrelevant alternatives' or 'Pareto optimality' or anything else. Only one guy matters. Talk of voting systems is stupid.
Did Sen really believe that Arrow's Dictator had power over others? Or did he not understand that the word 'Dictator' in English means a guy like Hitler or Stalin as opposed to someone who knows and votes for what is best for Society but who has no other power?
We cannot begin to understand the intellectual challenge involved in Arrow's impossibility theorem without coming to grips with the focus on informational inclusiveness that goes with a democratic commitment, which is deeply offended by a dictatorial procedure. This is so, even when the dictatorial result is entailed by axiomatic requirements that seem reasonable, taking each axiom on its own.
A guy votes for a set of things. It turns out that the SWF chooses the same set of things. The guy didn't make the SWF choose those things. Where is the 'dictatorial procedure'? Why should anyone take offence? The thing could have happened by chance. Or it might result from this guy being genuinely more altruistic and knowledgeable than anyone else. It is political correctness gone mad to label someone wiser and better than others as a Dictator simply because there is an objective reason to think that person should be the Dictator. It's like taking offence at 'Brown privilege' on the basis that Brown people could have established hegemony over White people and therefore they actually did so and are thus guilty of a terrible crime and should just shut the fuck up while we moan about the horrible oppression they hypothetically could have inflicted.
What should an altruistic and omniscient voter do to avoid the charge of 'Dictatorial procedure' under an ideal voting system? Should he abstain from voting? But then 'informational inclusiveness' and 'democratic commitment' would go out of the window! We can't exclude a guy from voting because his vote is virtuous and well-informed. We have to let him vote even if he is stupid and vicious because that's 'informational inclusiveness'. Similarly 'democratic commitment' means feeling you have a duty to vote- even if you are smarter and more altruistic than others.
Now, it may be, that Arrow's result has some occult, culturally specific, meaning which has to do with the refugee Ashkenazi Anarchist tradition- perhaps Arrow was mathematicizing Rudolf Rocker's (who was not himself Jewish) 'Nationalism & Culture' as an argument against any sort of 'Organicist' Bergsonian SWF- and maybe, in line with some hints from Aumann, this has deep roots in Sanhedrin judicial hermeneutics such that even the 'bat kol'- the voice from Heaven revealing Divine Truth- must be excluded from a particular Social process of Deliberation.
Still, we must admit, Hindu India has no similar tradition. If Sen was enraptured by Arrow's theorem, it was because he was too stupid to understand or too dishonest to acknowledge what is universally meant by the word 'Dictator', not because there existed some deep aporia in the Bengali collective psyche, or some shibboleth in its cultural heritage, or some repeated trauma in its political history, analogous to a certain strain in Ashkenazi Anarchism in the troublous first half of the Century.
True, both the antagonomic or ontologically dysphoric, perpetually kvetching, Yiddish Maven and the endlessly verbose, pointlessly argumentative, Bengali Babu were considered a little too big for their boots but, the fact is, times have changed. The Jews have done very very well politically and economically, and, truth be told, transformed the Sciences and the Arts. By contrast, Bengal has stagnated, it has gone backwards. Sen's Presidency College, for purely political reasons, has been in a state of continuous decline longer than I've been alive.
This does not mean all academics are worthless or that they should be excluded from any forum where grown-ups talk. Since discourse- public or otherwise- has no means to rule out a priori the possibility that it mightn't be utterly worthless, Arrowvian Dictators, incarnating a Bergsonian SWF, we may always have with us. However, they can't silence Sen-tentious drivel. So such Arrowvian Dictators are useless.
True, if you are really interested in the informational foundations of Economic or Political mechanisms, Arrow's theorem does open doors. It helps you to see the homology between preference revelation problems, agenda control problems, concurrency problems, problems of too much or too little preference diversity, problems of 'dynamic turbulence', hysteresis and ergodicity, Signalling, Coordination and Evolutionary Game Theoretic problems, problems relating to computational complexity classes- all sorts of problems become mutually illuminating. However these problems motivate research programs which increase 'efficiency' in the use of resources. They yield 'value free' objective agreements of a type that motivate the notion of a Social Welfare Function. They aren't a pure waste of time. Thus, they are 'Dictatorial' in an Arrowvian sense, more particularly as extended by Sen. But the corollary is- Democratic 'inclusiveness' requires we shun such work. Better tell stupid lies instead.
Proof of the General Possibility Theorem: By the Pareto Principle the set of all individuals is decisive. By the Contraction of Decisive Sets, some proper subset of all individuals must also be decisive. Take that smaller decisive set, but some proper subset of that smaller set must also be decisive. And so on. Since the set of individuals is finite, we shall arrive, sooner or later, at one individual who is decisive. But that violates the Non-dictatorship condition. Hence the impossibility.
If everyone agrees on something, our Dictator (who knows and wants what everybody will later say was the best Collective decision but who is deemed to reverse his preference) will be the single vote against it. The Pareto Principle has no purchase. 'Contracting the decisive Set' is fruitless. There is no impossibility result because our omniscient and benevolent Sage is deemed to have reversed his preferences. Thus he doesn't fit the criterion for an Arrowvian dictator.
It seems obvious, now, that Sen's contributions to Econ. were either senseless or self-defeating. Still, from a narrowly Academic perspective, since Arrow himself went through Sen's 1970 'Collective Choice & Social Welfare', it is a canonical work.
This theorem (Arrow's Impossibility result) implies that if everyone prefers to have a deterministic Vote aggregating system which everybody agrees delivers results that are the 'best' in some objective, value-free, sense, though they may not be able to at all 'quickly' work out all the steps by which the result was arrived at, (i.e. there is only NP solvability) then, if this system were implemented, it wouldn't be Democratic at all. What we would actually have is a Dictatorship!
This theorem is easy to prove iff we define 'Dictator' as a guy who wants and knows what is best for Society- perhaps by some non deterministic procedure, or superior Ethical intuition or 'Divine' inspiration- and therefore makes the same choices as the ideal Bergsonian SWF or Perfect Voting rule. Clearly, the theorem is now a tautology- it poses no scandal unless we think P=NP in which case it is a puzzle as to why a deterministic SWF can't get the same result as a possible voter able to use non-deterministic methods. If, as is likely, P is not equal to NP, there is no scandal- just a tautology of a misleading and disingenuous kind.
Still, one can't deny, this is a very wonderful theorem because it can be also be used to prove the impossibility of my neighbour 's cat iff we define the tabby in question as an Arrowvian method of aggregating preferences which must satisfy certain 'seemingly reasonable' conditions specifically chosen so that the thing is impossible because one of the conditions is not reasonable at all but rather is utterly mad. Of course, we could achieve the same end just by lying. But where's the fun in that?
Sen's greatness lies in his deployment of certain bien pensant caveats which suggests that considerations of Social Welfare exceed economics and involve philosophical issues which may cash out as value judgements, or Samuelson type 'ethics', but not yet, never yet. Instead we should indulge in a type of 'Deliberative Democracy' which never decides anything, preferring instead to just go on repeating platitudes couched in specious arguments and supported by bare-faced lies.
However, if philosophical issues really have salience- i.e. if some process of Public Reason can change Preferences, or motivate meta-preferences, in a manner such that, under ideal- perhaps Rawlsian- conditions, everybody would want the same outcome for Society- then, there could be a Platonic Guardian or Benthamite Oracle or Newcombe Predictor who arrived at the same conclusion independently.
Since, by definition, such a person would be stigmatised as a Dictator if included in the voting process- and Arrow doesn't allow us to exclude such a person- Arrowian Non-Dictatorship would not be a desirable property for a Collective Choice mechanism to boast. Why? Because it specifically bars the sort of outcome which would make it otherwise desirable.
Had Sen simply said 'Arrow's SWF is not at all isomorphic to a Bergson-Samuelson type SWF and proves nothing except that if you define something which aint Dictatorial as Dictatorial all you have done is utter a stupid lie' then he wouldn't have gotten to an Academic position where he could tell stupid lies about the true cause of the Bengali famine without being laughed at in Oxford or spat upon in Calcutta.
Perhaps Sen couldn't, in good conscience, say any such thing. Maybe, he genuinely thinks Arrow's result implies something very important about the nature of Democracy- viz. that it is shite and so we should all continually talk shite coz that's Democratic and Civilised people are democratic so just get with the program and start talking shite immediately you great big Bengollywog you. Don't let the side down. The World is watching.
He wrote-
The informational foundation of modern social choice theory relates to the basic democratic conviction that social judgements and public decisions must depend, in some transparent way, on individual preferences, broadly understood.
What about the notion that 'Social judgements must depend on individual preferences' ?
Is that what a truly modern social choice theory would counsel?
Nope. To reduce vulnerability to predators and parasites, human beings should always try to baffle any preference revelation mechanism. Indeed, not knowing one's own preferences is a safer strategy- which is why Evolution has ensured that there is no Momus window into the heart even for one's own ego.
Similarly, it is better to have Social Judgements which are robust to moment to moment changes in preferences so that the Regulatory or Normative environment is predictable and reduces Uncertainty in formulating long term plans.
Since, Newcombe type problems have salience in many Social and Economic processes, Preference falsification shouldn't be cognitively dissonant- and, indeed, the evidence is, it isn't. Pedagogues who write books are constantly astonished that people are inconsistent. They may support Liberty for themselves but not for others whom they exploit. Such pedagogues attribute causality to soi disant Great Men who wrote some pamphlet long ago descrying this inconsistency. However, such people were dismissed as antagonomic cranks who were either guillotined or condemned to the Bastille of Pedagogy or whose heads were lost to the community by some self-selective process of impressment into the condition of being the galley slave of a Scholarship long since run aground.
Nobody does not know, it is cognitively costly to have rational, or even alethic, preferences over all Social options though 'self deception' in this respect is an Evolutionarily Stable Strategy. Indeed, for analogous reasons, regret minimisation would militate for big saltations or discontinuities in Preference profiles. Meta-preferences should link to Tardean mimetic rules of a certain sort so that there is canalistion and capacitance diversity.
Ultimately, we have to recognise Preferences are just metaphysical tosh- like Utility functions. Social judgements shouldn't be based on them. Rather, there are canons specific to Judgement that collective Jurisprudence too should adhere to. The same point may be made about Public Decisions. To make them dependent on individual preferences is stupid. Rather they should conform to the canons specific to Public Administration. This is not to say that Information aggregation isn't important. It is, but more important yet is that Public Decisions are free of ambiguity, Agenda control problems, race hazard or concurrency problems and so forth.
Arrow's resurrection of Condorcet in the early Fifties has a certain Historical and Cultural significance. No doubt, back then, there was some point to pretending that mathematical logic could serve an ideological purpose. After all, at that time, Command Economies were spreading faster than Market economies. In the Sixties, following China's humiliating defeat of India, more and more ex-Colonies were choosing to go down the 'One-Party' path.
Those days are long gone. The Berlin Wall fell before Sen got his Nobel. But the Hayekian writing on the wall was clear to see by the beginning of the Eighties- i.e. the last time Arrowvian Social Choice Theory had a pulse. Since then, Chichilnisky and Saari have given us a notion of 'topological dictators' where utility functions are continuous. but the interpretation of the notion has nothing to do with 'Dictatorship' as opposed to Banzhaf Coleman type voting power.
Currently, Democracy and the Rule of Law are sufficiently attractive in their own right. Mathematical logic can be excused the duty of telling stupid lies in this respect. Why? Rather than prove the existence of God, as in Godel, or the Hitler in the ballot box, as in Arrow, it has genuinely alethic, and therefore useful, things to do.
Sen doesn't. He is still saying shite like this- The emergence of this democratic instinct relates closely to the ideas and events that surrounded the European Enlightenment. Even though the pursuit of democratic social arrangements drew also on various earlier sources and inspirations, it received a definitive delineation and massive public acknowledgement only during the Enlightenment, particularly - but not exclusively - during the second half of the eighteenth century, which also saw the French Revolution and American independence...
Good to know that darker skinned people lacked any such 'democratic instinct'.
Why?
Obviously, darkies belong to a different species.
That's why they have different 'instincts'.
However, History teaches us that White people, too, lacked such instincts.
'In contemporary social choice theory, pioneered by Kenneth Arrow, this democratic value
is absolutely central, and the discipline has continued to be loyal to this basic informational
presumption. For example, when an axiomatic structure yields the existence of a dictator as a
joint implication of chosen axioms that seemed plausible enough, this is
immediately understood as something of a major embarrassment for that set of axioms, rather
than being taken to be just fine on the ground that it is a logical corollary of axioms that have
been already accepted and endorsed.Why?
Obviously, darkies belong to a different species.
That's why they have different 'instincts'.
However, History teaches us that White people, too, lacked such instincts.
There never has been any, not utterly evanescent, polity where 'Social Judgements' and 'Public Decisions' were not 'protocol bound', subject to 'artificial reason' and wholly robust to changes in individual preferences save by Executive action whether ab ovo legitimate or retrospectively made so. Condorcet perished along with his chimeral mathematical schemes, while the seed of the lawyer John Adams went from strength to strength.
From time to time, a polity may decide that a particular Social Judgement or Public Decision should be made in a way which transparently depends on individual preferences. However the power to make that decision is not itself dependent on 'individual preferences'. It is dependent on authority granted by due process of Law. Whatever the outcome of any Social Choice process- whether it involve preference aggregation or not- it remains the case that it is subject to legal challenge and Judicial review. That's why, contra Sen, a Paretian illiberal is impossible- if 'self ownership' is a Liberal value. Even if everyone wants something abolished- e.g. my right to write this shite which I'd much rather not write so as gain greater utility by whining about the great injustice I've suffered by not being allowed to ventilate my impartial ignorance on this and every other issue- it still can't be abolished save if the Rule of Law is usurped by an arbitrary Dictatorship of some sort.
From time to time, a polity may decide that a particular Social Judgement or Public Decision should be made in a way which transparently depends on individual preferences. However the power to make that decision is not itself dependent on 'individual preferences'. It is dependent on authority granted by due process of Law. Whatever the outcome of any Social Choice process- whether it involve preference aggregation or not- it remains the case that it is subject to legal challenge and Judicial review. That's why, contra Sen, a Paretian illiberal is impossible- if 'self ownership' is a Liberal value. Even if everyone wants something abolished- e.g. my right to write this shite which I'd much rather not write so as gain greater utility by whining about the great injustice I've suffered by not being allowed to ventilate my impartial ignorance on this and every other issue- it still can't be abolished save if the Rule of Law is usurped by an arbitrary Dictatorship of some sort.
In any case, the fact is, no Direct or 'Deliberative' Democracy has ever existed.
There has only ever been either the Rule of Law or a Dictator whose word was such.
It is a separate matter that the dynamic benefits gained from the power to raise taxes at low cost of coercion have worked to extend the franchise in certain types of market economies. However, if public goods vital to the continuance of the polity can be paid for some other way- e.g. by a natural resource endowment- there is no biologically ordained or culturally determined 'democratic instinct' in the background militating for effective Democracy- no matter what the Constitution requires. No country has achieved or sustained Democracy without taxing its voters. Some States have greatly enriched their subjects but, so long as those subjects aren't paying for Public goods- no effective, as opposed to cosmetic, self-sustaining Democratic transition has occurred.
That's why Putin's Russia is the way it is. It's also why Modi is trying to get the poor into the tax/transfer net. He knows India doesn't have a natural resource endowment. The only way kids as poor as he was can come up is if they pay the taxes which fund their civilizational rise.
No axiomatic structure yields the existence of a dictator 'as a joint implication of chosen axioms'. Arrow defined a possible voter who always agrees with the Bergsonian SWF as a dictator. He arbitrarily restricted the SWF to the class of deterministic functions but allowed profiles to be non-deterministically verifiable solutions to the SWF. Clearly there is a P/NP type problem here and if Social Choice theory hadn't died long ago this would be the focus of research. Arrow's method doesn't make any stipulation about the time class of solutions so it has no real world application. But for that same reason, we know it to be tautological nonsense featuring semantic dishonesty. His 'Dictator' arises from one of his axioms. It didn't arise from any combination of the others. It is independent, utterly arbitrary, and thus itself quintessentially 'Dictatorial'.
By Dictator, in ordinary English, we mean a guy who has power over others. What Arrow is describing could be a mute or accidental Oracle who has no power. Alternatively, his 'Dictator' could be a Judas Goat or even, as D.G.Saari suggested, a sort of social chameleon like Woody Allen in Zelig.
If there is a Dictator in the common acceptation of the word, it would be a foolish waste of time to aggregate preferences or stipulate for 'independence of irrelevant alternatives' or 'Pareto optimality' or anything else. Only one guy matters. Talk of voting systems is stupid.
Did Sen really believe that Arrow's Dictator had power over others? Or did he not understand that the word 'Dictator' in English means a guy like Hitler or Stalin as opposed to someone who knows and votes for what is best for Society but who has no other power?
We cannot begin to understand the intellectual challenge involved in Arrow's impossibility theorem without coming to grips with the focus on informational inclusiveness that goes with a democratic commitment, which is deeply offended by a dictatorial procedure. This is so, even when the dictatorial result is entailed by axiomatic requirements that seem reasonable, taking each axiom on its own.
A guy votes for a set of things. It turns out that the SWF chooses the same set of things. The guy didn't make the SWF choose those things. Where is the 'dictatorial procedure'? Why should anyone take offence? The thing could have happened by chance. Or it might result from this guy being genuinely more altruistic and knowledgeable than anyone else. It is political correctness gone mad to label someone wiser and better than others as a Dictator simply because there is an objective reason to think that person should be the Dictator. It's like taking offence at 'Brown privilege' on the basis that Brown people could have established hegemony over White people and therefore they actually did so and are thus guilty of a terrible crime and should just shut the fuck up while we moan about the horrible oppression they hypothetically could have inflicted.
What should an altruistic and omniscient voter do to avoid the charge of 'Dictatorial procedure' under an ideal voting system? Should he abstain from voting? But then 'informational inclusiveness' and 'democratic commitment' would go out of the window! We can't exclude a guy from voting because his vote is virtuous and well-informed. We have to let him vote even if he is stupid and vicious because that's 'informational inclusiveness'. Similarly 'democratic commitment' means feeling you have a duty to vote- even if you are smarter and more altruistic than others.
Now, it may be, that Arrow's result has some occult, culturally specific, meaning which has to do with the refugee Ashkenazi Anarchist tradition- perhaps Arrow was mathematicizing Rudolf Rocker's (who was not himself Jewish) 'Nationalism & Culture' as an argument against any sort of 'Organicist' Bergsonian SWF- and maybe, in line with some hints from Aumann, this has deep roots in Sanhedrin judicial hermeneutics such that even the 'bat kol'- the voice from Heaven revealing Divine Truth- must be excluded from a particular Social process of Deliberation.
Still, we must admit, Hindu India has no similar tradition. If Sen was enraptured by Arrow's theorem, it was because he was too stupid to understand or too dishonest to acknowledge what is universally meant by the word 'Dictator', not because there existed some deep aporia in the Bengali collective psyche, or some shibboleth in its cultural heritage, or some repeated trauma in its political history, analogous to a certain strain in Ashkenazi Anarchism in the troublous first half of the Century.
True, both the antagonomic or ontologically dysphoric, perpetually kvetching, Yiddish Maven and the endlessly verbose, pointlessly argumentative, Bengali Babu were considered a little too big for their boots but, the fact is, times have changed. The Jews have done very very well politically and economically, and, truth be told, transformed the Sciences and the Arts. By contrast, Bengal has stagnated, it has gone backwards. Sen's Presidency College, for purely political reasons, has been in a state of continuous decline longer than I've been alive.
Why?
Bengali public discourse has gotten stupider and stupider, less and less alethic, more and more gestural, yet, because it has never bottomed out as a scurrilous Socioproctology but rather kept up a shabby genteel pretence of rationality and a veneer of Western scholarship, it retains a certain meretricious fungibility.
Thus, Sen could still have helped turn things round a little after he got his Nobel.
He chose to go in the other direction.
Every Bengali knows that Bangladesh was a democracy in 1974.
1.5 million died in a terrible famine.
In 1979 and 1984, Bangladesh was more of a dictatorship. Yet famine was averted.
This didn't stop Sen from idiotically bleating 'Famine can't happen in a Democracy'.
Why?
Aren't Bengalis human beings?
If they elect a Government in free and fair elections- why can't they be called a Democratic people?
Every Bengali knows that Bangladesh was a democracy in 1974.
1.5 million died in a terrible famine.
In 1979 and 1984, Bangladesh was more of a dictatorship. Yet famine was averted.
This didn't stop Sen from idiotically bleating 'Famine can't happen in a Democracy'.
Why?
Aren't Bengalis human beings?
If they elect a Government in free and fair elections- why can't they be called a Democratic people?
Sen and Nussbaum's contribution to 'Deliberative Democracy' is the tolmema of telling stupid lies.
True, if you are really interested in the informational foundations of Economic or Political mechanisms, Arrow's theorem does open doors. It helps you to see the homology between preference revelation problems, agenda control problems, concurrency problems, problems of too much or too little preference diversity, problems of 'dynamic turbulence', hysteresis and ergodicity, Signalling, Coordination and Evolutionary Game Theoretic problems, problems relating to computational complexity classes- all sorts of problems become mutually illuminating. However these problems motivate research programs which increase 'efficiency' in the use of resources. They yield 'value free' objective agreements of a type that motivate the notion of a Social Welfare Function. They aren't a pure waste of time. Thus, they are 'Dictatorial' in an Arrowvian sense, more particularly as extended by Sen. But the corollary is- Democratic 'inclusiveness' requires we shun such work. Better tell stupid lies instead.
Now to dispose of Sen's proof of Arrow's theorem.
Adopt a convention such that any Arrowvian Dictator is deemed to have reversed his preferences for the purpose of aggregation. (Alternatively, allow the SWF to be non-deterministic while preserving 'anonymity') Then everything will be hunky dory. Proof of the General Possibility Theorem: By the Pareto Principle the set of all individuals is decisive. By the Contraction of Decisive Sets, some proper subset of all individuals must also be decisive. Take that smaller decisive set, but some proper subset of that smaller set must also be decisive. And so on. Since the set of individuals is finite, we shall arrive, sooner or later, at one individual who is decisive. But that violates the Non-dictatorship condition. Hence the impossibility.
If everyone agrees on something, our Dictator (who knows and wants what everybody will later say was the best Collective decision but who is deemed to reverse his preference) will be the single vote against it. The Pareto Principle has no purchase. 'Contracting the decisive Set' is fruitless. There is no impossibility result because our omniscient and benevolent Sage is deemed to have reversed his preferences. Thus he doesn't fit the criterion for an Arrowvian dictator.
Stuff like this is puerile but then Professors are paid to prolong neoteny.
Economics, at least in India, faced a Credentialist crisis.
Too many graduates chasing too few bureaucratic berths.
Lectures on this type of shite served a warehousing function.
Kaushik Basu remarks that the Delhi School of Economics (this was in the economically stagnant and deeply disillusioning Sixties) had become a centre for Social Choice theory- or rather for such cowardly Careerism as chose to instrumentalize that mendacious availability cascade so as to shirk all Social Responsibility or Patriotic Duty and high tail it for Greener Pastures- and that he himself, as a graduate student at the LSE was asked by Prof. Morishima whether he intended to specialise in 'India's subject'- i.e the type of Econ which kept Indians malnourished while Japan rose and rose.
By the early Eighties, Social Choice- always useless- was clearly dead and so Basu and his ilk flourished in some equally arcane but less obviously inutile field.
Meanwhile Sen's own approach- his version of 'public discourse'- was increasingly seen to be part of the problem because it made policy space multi-dimensional and thus gave salience to 'agenda control' as predicted by the McKelvey Chaos theorem. Put bluntly, this meant that playing the 'Equity' card was not proof of higher Ethical standing but just part of a corrupt rent-seeking racket or a bureaucratic buck passing strategy. Hurwicz's Mechanism Design, however, could continue to burgeon but Philosophy's intrusion into the Economist's domain merely added noise to signal. Sen himself was seen as a well meaning but ineffectual Mother Teresa- a figure to be venerated not emulated. Pakistan's Dr. Ruth Pfau- a trained Doctor specialising in leprosy- on the other hand, is a nun whose medical work is valuable in itself. Nobody would compare Sen to Dr. Pfau. But then Pfau isn't eligible for a bogus Nobel.
By the early Eighties, Social Choice- always useless- was clearly dead and so Basu and his ilk flourished in some equally arcane but less obviously inutile field.
Meanwhile Sen's own approach- his version of 'public discourse'- was increasingly seen to be part of the problem because it made policy space multi-dimensional and thus gave salience to 'agenda control' as predicted by the McKelvey Chaos theorem. Put bluntly, this meant that playing the 'Equity' card was not proof of higher Ethical standing but just part of a corrupt rent-seeking racket or a bureaucratic buck passing strategy. Hurwicz's Mechanism Design, however, could continue to burgeon but Philosophy's intrusion into the Economist's domain merely added noise to signal. Sen himself was seen as a well meaning but ineffectual Mother Teresa- a figure to be venerated not emulated. Pakistan's Dr. Ruth Pfau- a trained Doctor specialising in leprosy- on the other hand, is a nun whose medical work is valuable in itself. Nobody would compare Sen to Dr. Pfau. But then Pfau isn't eligible for a bogus Nobel.
Why did Sen, a patriotic Indian who felt hurt by the suffering of the poor, end up championing failed policies and telling stupid lies? He wasn't really a Communist- indeed, he appears to be a Classical Economist living down a Benthamite predisposition. Why could he not 'speak truth to power'?
Perhaps Sen- as an undergraduate at Presidency didn't understand the Tarskian background to Arrow's theorem when he first chanced upon it. It cast a glamour upon him because he wasn't up to speed- few were, back then- on mathematical logic. Essentially, Arrow was doing something like Kripke (1975) who showed that a formal Language can contain its own Truth Predicate but in a manner that doesn't defeat Tarski but rather illuminates his result. Similarly, Arrow's reckless disregard for the truth in using phrases like 'Non-Dictatorship' or 'Social Welfare Function' is what gave his theorem its seemingly magical property. The Tarskian truth remains that there may be some non-deterministic, ineffable, procedure outside the Language- it may be in its meta-language- which could incarnate as an Oracle function within it- but we couldn't prove, for any given case, this was so. Thus Arrow's Non-Dictatorship might be like a restriction on a non deterministic Turing machine or oracle within the set of preference profiles and thus may be of continuing interest, though this is not something the extant literature has concerned itself with.
The blog 'a fine theorem' has a well researched article on Arrow from which I quote-
'The usual story is that Arrow’s work on social choice came out of his visit to RAND in 1948. But this misstates the intellectual history: Arrow’s actual encouragement comes from his engagement with a new form of mathematics, the expansions of formal logic beginning with people like Peirce and Boole. While a high school student, Arrow read Bertrand Russell’s text on mathematical logic, and was enthused with the way that set theory permitted logic to go well beyond the syllogisms of the Greeks. What a powerful tool for the generation of knowledge! His Senior year at CCNY, Arrow took the advanced course on relational logic taught by Alfred Tarski, where the eminent philosopher took pains to reintroduce the ideas of Charles Sanders Peirce, the greatest yet most neglected American philosopher. The idea of relations are familiar to economists: give some links between a set (i.e, xRy and yRz) and some properties to the relation (i.e., it is well-ordered), and you can then perform logical operations on the relation to derive further properties.'
... A great theorem due to the Polish mathematician Szpilran, and I believe popularized among economists by Blackwell, says that if you have a quasiorder R that is transitive, then there exists an order R’ which completes it. In simple terms, if you can rank some pairs, and the pairs you do rank do not have any intransitivity, then you can generate a complete rankings of all pairs which respects the original incomplete ordering. Since individuals have transitive preferences, Pareto ranks are transitive, and hence we know there exist social welfare functions which “extend” Pareto.
The Szpilrajn extension theorem, which Blackwell brought to Arrow's attention and which, perhaps, motivated the latter's admission that he hadn't really killed off the Bergson SWF, depends on the 'Axiom of Choice' or equivalently 'Zorn's lemma' or 'the well-ordering theorem'. Even if we have no philosophical objection to this (i.e. we don't mind 'Banach-Tarski type weirdness or the manner in which any deterministic partial order is magically extended, perhaps by some non deterministic process, into a well-ordered set or continuous utility function) it is still the case that the sort of problems which it is useful for Economist's to work on- like the 'reverse game theory' that is mechanism or auction design- fall within the ambit of Friedman's 'Reverse Mathematics' project. Wikipedia says this approach 'starts with a framework language and a base theory—a core axiom system—that is too weak to prove most of the theorems one might be interested in, but still powerful enough to develop the definitions necessary to state these theorems. ...
'For each theorem that can be stated in the base system but is not provable in the base system, the goal is to determine the particular axiom system (stronger than the base system) that is necessary to prove that theorem'
Natural language discussion- e.g. the Socratic dialogues- proceeds in this manner. Embedding Social Choice in a 'Reverse Mathematics' Research project means there is no discontinuity between 'Philosophy' and 'Economics'. Policy space doesn't become multi-dimensional. There is no problem with Agenda Control.
Similarly, in Linguistics, the Chomskian notion that an 'i-language' exists- i.e the opinions of educated native speakers re. correct usage can be collected and systematised so an 'ideal' 'intensional' language is established as the proper object of study such that something like 'ECP' violation becomes as serious a scandal as CPT violation in Physics- this notion isn't really a step forward. It is a chimera, a mirage. It hasn't raised Language to the level of Physics. Rather it has made Syntax independent of Semantics. An i-language may exist, but the condition for its existence is that it is entirely meaningless.
Sen was a hardworking and smart guy. But he was greatly conscious of India's inferiority. His work on famines was worthless and he lied about it- but then starving people aren't important- that's why, according to him, some Bengalis ate 5 times as much rice during the Famine as they did before thus callously condemning other Bengalis to starve.
Ken Arrow, however, was important- he was a top Professor related to other top Professors. Sen didn't distort Arrow. He was not intellectually dishonest. He saw that the Arrowvian program for Welfare Economics was going nowhere. It was dead in the water even if no preference-revelation problems arose. But it was still 'Western' and 'Democratic'.
Sen's solution was worse than the disease. He chips away at the Pareto condition- the one thing everybody can agree on- and brings back 'value judgements' without resurrecting Samuelson's ethical program- this is Philosophy in its most bogus form, i.e. this is 'agenda-control' based rent-seeking sophistry- and does not change course though very much in the loop re. McKelvey & Schofield & Ostrogorski & Anscomb & Saari & Chichilnisky et al.
I am not saying Sen did anything wrong. He was an academic and that's what academics do- which is why we consider them drudges and donkeys. It wasn't his fault, his chosen field had turned moribund. Everyone assumed Sen had found himself another niche- something to do with saying 'guys, lets stop being dicks and just help poor and starving people already'- or that he was actually a Philosopher or maybe that he knew about ancient Indian thought.
But that was precisely the problem. The Indians too- including people like me- thought he must be capable of saying sensible stuff. He wasn't. He talked worthless self-regarding shite and made truly horrible policy prescriptions. His career as Chancellor of Nalanda University revealed him to be on a par with the most useless and corrupt of our own homegrown academic thugs. True, he ensured that the PM's daughter's friends got very well paid sinecures. That was right and proper and in keeping with Indian best practice. But, when a new PM came in, those ladies couldn't have their contracts extended in violation of the Charter because they had failed to get themselves powerful backers while the going was good.
Sen thinks 'autonomy' means 'keep the ex-PM's daughter's chums in office though it is illegal to do so and they have failed to secure political backing' and that such 'autonomy' turns a University- even one located in rural Bihar- into an international powerhouse. This isn't the case. Sen failed to get autonomy when it would have benefited his proteges. Why harp on the subject now that the other party has got its own man in as Chancellor?
Sen thinks 'autonomy' means 'keep the ex-PM's daughter's chums in office though it is illegal to do so and they have failed to secure political backing' and that such 'autonomy' turns a University- even one located in rural Bihar- into an international powerhouse. This isn't the case. Sen failed to get autonomy when it would have benefited his proteges. Why harp on the subject now that the other party has got its own man in as Chancellor?
Things didn't have to go down this way. Sen could have embraced evolutionary game theory, like Binmore, and ended up showing the Govt. of India how to raise billions from Spectrum auctions. At the very least, he could have uttered 'truth to power' about the failures of the Public Education & Health System. But, he was afraid of the Left and chose, instead, to talk utter nonsense. He was quite close to the previous administration. Yet he says that his old colleague, Manmohan Singh, tried to turn India into a global economic power with a sick and uneducated workforce. Sen doesn't explain why Manmohan Singh was so cruel and stupid. No doubt, Sen thought he was criticising the new PM- Narendra Modi. But Modi isn't a friend of Sen's. Sen doesn't know what Modi is or is not trying to do. He did know what Singh was trying to do. Thus his stricture can only apply to Singh not Modi.
Sen, like Chomsky, has turned into a fake news guy because of intellectual grandiosity of a technical kind. He chose to take as his subject a Szpilrajn extended set which assumed the axiom of choice but which failed to account for the possibility this introduced- viz. Non Dictatorship will be violated by a non-deterministic Oracle (with a particular 'maximal' property) which must necessarily exist, though, realistically, it may be inaccessible for in a much higher complexity class. It is precisely the informational foundation of the subject which this grandiosity has destroyed in advance.
Chomsky did something similar to defend the question begging notion of an 'i-language'. In other words, these two famous atheists first turned their subject into something God-like in its set theoretic properties and then became reconciled to saying it was meaningless save in some special sense known only to themselves and thus still part of 'Public reasoning'.
Chomsky did something similar to defend the question begging notion of an 'i-language'. In other words, these two famous atheists first turned their subject into something God-like in its set theoretic properties and then became reconciled to saying it was meaningless save in some special sense known only to themselves and thus still part of 'Public reasoning'.
By contrast, 'Reverse Math', doing useful things with more parsimonious axioms is a good way forward which meshes well with what increased computing power and 'Big Data' allows smart people to do. But then Evolution itself takes this humble, regret minimising, route. No doubt, the fitness landscape is multi-dimensional but there is a workaround in terms of canalisation and capacitance diversity.
Something similar saves Public Discourse from Manichaean stasis or Corrupt 'Agenda Control' or buck passing concurrency deadlock. Why? Because people move on with their lives. Publicity Hungry Pundits can ignore how people vote but they can't ignore falling book sales. They have to jump on a Fake News bandwagon and advertise their meretriciousness more nakedly than every before.
A few hours after Ken Arrow's death was announced, this is Sen talking up the re-issue of his old book-
Sen begins by pretending that his 1970 book was concerned with what was actually happening in 1970. It wasn't. It was wholly abstract. It might have been a prediction of the sort of political processes which might obtain once 'the State had withered away' and Socialism had been established. It had no connection at all to American or British or Indian politics.
Public reasoning can't be Academic reasoning if the latter is based on an intensional language or relies crucially on things like Szpilrayn's theorem and therefore the axiom of choice. Why? Public reasoning must be in a natural language whose acceptations are common knowledge. Even if the public is super smart, its metaphysics must still be parsimonious and its semantics extensional. Otherwise well formed sentences in its language will be verifiably meaningless save adventiously or by means of an Oracle.
Trump may well have been wrong on the state of the US economy just as Kennedy was wrong about the 'missile gap'. So what? That's not why he was elected. No Trump voter is now saying 'whoops. I thought unemployment was rising so I voted for a guy with strange hair and an orange tan because...urm, that's what smart people do, right?'
Why does Sen assume that rational people will vote for an elderly property developer who has never held any sort of Govt. job or political office in his life just because they think that Unemployment is rising?
Is Sen a misogynist? Does he think that a woman in the White House would be incapable of reducing Unemployment despite being a Democrat? Even if Sen is a misogynist, why does he assume that the American voter shares his view?
Sen can't reason- at least in public- can he state verifiable facts? Asked about Modi's demonetisation, he says-
The Govt. gains seigniorage through demonetisation. It is a tax. It yields a very large dividend- one sufficient to implement a 'Basic Income' type cash-transfer which, by the second fundamental theorem of Welfare Econ, is allocatively efficient and, perhaps, India's only hope of of implementing a Social Minimum. Poor Indians are cash poor. Even Sen must know this. This isn't a regressive tax, though no doubt poor implementation may make it so for some. Notice, Sen isn't focusing on poor implementation. He is saying the idea is senseless in itself.
Why is Sen lying? Why is he saying it can't yield a dividend? Does he mean that the monetary shock will be so severe that tax revenue will fall? He knows that won't happen. So he isn't saying that. He's just lying is all.
Perhaps you think I'm being too hard on a senile man. Maybe he doesn't realise that '86 percent' of the monetary base isn't really being destroyed. But, this isn't actually the case is it? His own remarks show that he knows that those who came by their cash honestly can exchange old notes for new ones. Those who didn't will take a hit.
Longer term, this will tip Indians to move towards mobile banking. Vested interests- of a sort ordinary Indians come across in their day to day life- want briefcases of cash. They will have to find a new modus operandi. The State has an opportunity, which may be frittered away, to change the fiscal equation. I don't know the outcome. Nor does Sen. But Sen is willing to tell lies about it.
Why?
He's a shill for a Academic Ponzi scheme repackaging a worthless book he wrote in 1970.
Okay. Fair enough. That's Globalisation for you- just Capitalism at work- so what?
Well, actually there's a tragic twist to this tale
It hasn't.
Sad.
Okay. Fair enough. That's Globalisation for you- just Capitalism at work- so what?
Well, actually there's a tragic twist to this tale
Arrow, as a young man, made his name by using what had become a highly emotive word- viz. 'Dictator' -in a dishonest way. He was trying to get the ethics out of Welfare Econ by unethical means while pointing to a type of Maths which in time would become genuinely important. Suppose he'd used the word 'Paedophile' instead. Then, Sen and other young Bengalis- who for historical reasons thrilled to the word 'Dictator' but, quite rightly, experienced no similar frisson at the term 'kiddy fiddler'- would not have written so much worthless nonsense nor would they now be habituated to telling such stupid lies. Instead, genuine Philosophers- motivated by Platonic dialogues like the Lysis and the Phaedrus- which are about fucking rich kids in the ass- would have taken up Arrow's theorem and that would be all right because they'd now be in jail having their heads kicked in, all of which only goes to prove true Democracy can guard us against Famine. Or if not Famine, at least it can do the washing up.
Just checked.It hasn't.
Sad.
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