Saturday, 8 November 2014

Alan Kirman & the Impossibility of a Paretian Illiberal

This has been edited in the light of a comment.

It isn't possible to believe Pareto improvements- i.e situations where a guy can report being made better off without anyone else reporting being made worse off- are desirable without also believing all agents are sovereign over at least one choice affecting themselves- i.e. a Paretian Illiberal, of the Amartya Sen type, is impossible. Assuming unrestricted domain, this becomes trivially true by introducing a notion of doxastic self-ownership- for e.g. by valorising the preference to have one's own preferences.

Suppose a Paretian Liberal is impossible- in other words, Amartya Sen isn't a shithead- then it would be the case that a particular sort of rational being would
1) not prefer to have his own preferences and, worse still,
2) voluntarily subscribe to his own logical impossibility.
However, to do so isn't a Pareto improvement because the said Liberal could always chose to believe Sen is a shithead and thus be rescued from the fate of being logically impossible in a manner that makes no one else worse off- provided Sen is either himself a Paretian Liberal (in which case he either disproves his own existence or, and this result holds even if he isn't a Paretian Liberal, that he has hit upon an Acceptation for 'Paretian Liberal' which is wholly meaningless and thus he is talking shit and has shit for brains- which is why he is a shit-head) or else has a meta-preference not to be a shithead (in which case he can mend his ways) or else is too fucking stupid to ever grasp that he's a total shithead, in which case his feelings in this regard can't be hurt.

Truly unrestricted domain with 'nosey preferences' (i.e. which feature impredicativity) means we have an uncountable infinity of pair-wise choices which can't be well founded and so Sen's proof fails immediately. But this is scarcely a surprise. Impredicativity will do that to you.
Suppose I have a choice to either eat or not eat this biscuit. Permit me to have  meta-preferences- i.e. introduce impredicativity. I now can prefer to eat but prefer to prefer not to eat this biscuit (i.e. prefer to have ascetic preferences) or prefer to prefer to prefer to eat this biscuit (i.e. prefer to depass my ascetic preferences by reason of its sublation by a more refined notion of atraraxia) and so on and so fort. What is the upshot? Unrestricted domain with impredicativity of the type Sen stupidly imports (being insensitive to Arrow's Tarskian training) gives us something immediately bigger by a Godelian argument than its own acceptation (i.e. Unrestricted Domain can't mean whatever it was supposed to, thus no modal fixed points are available) and so, by Ackermann's Reflection principle, everything just got apophatic and nothing is well founded. But this isn't some wonderful new insight. It is simply childish.

A more serious reason to spurn Sen-tentious shitheadedness arises out of the manner in which 'Just So' representative individual type theories are wholly misleading.
Alan Kirman, explaining why mainstream Econ has fucked up so badly in recent years, explodes 'representative agent' models and asks us to shift our attention to Organisation, as opposed to Efficiency, as central to Social Science.
Kirman- a good guy who was once a Geography teacher- explains what is salient for Significs is that Impredicativity or Reflexivity does arise in Econ- which is why we can meaningfully speak of a Paretian Liberal- but this notion is only captured by interactions of an Organizational, i.e. second order, not Transactional, type. As a matter of fact, not theory, the Paretian Liberal does exist in all countries with the Rule of Law. Sen may say- boo to the Rule of Law, boo to Organization, boo to 'Niti'- but he can't deny that Paretian Liberalism is a better description of what obtains in Rule of Law, Democracies than his own Entitlement theory or Capabilities approach. The fact is, 'territoriality' or the 'bourgeois strategy in the hawk dove game' is evolutionarily stable and eusocial (vide Zahavi on the handicap principle) which is why it is the basis of Paretian Liberalism. True, this is not indefeasibly so but defeasibility is a good thing because, if Darwin not Dueteronomy is right, the future must always be, at least retrospectively as Popper and Dunnent and Huw Price have, albeit inadvertently, argued, not just unknown but radically unknowable. That last being, as Collingwood posthumously proves to his ageing Oakshotteian self, a distinction without a difference.


Anonymous said...

This is sheer stupidity. I'm amazed you actually emailed me this. What were you expecting? A pat on the back?
You keep harping on the fact that you went to the LSE. I have had first year students- not from the LSE but what you are pleased to refer to as my 'Godhulia Gornmnt College'- who have written more cogently on this topic.
Have you no shame?
I don't want to waste words on you so I will keep this brief- kindly look up terms you don't understand on Wikipedia. After all, all your vaunted Mathematical knowledge consists only of randomly cut and pasting stuff from there so you are already familiar with the relevant url.
1) Kirman is in General Equilibrium theory. Sen isn't. There is no connection between the two.
2) The generalised Lob's theorem explains why no proofs, one way or other, arise within any formalization of Social Choice theory. What you call impredicativity implies undecidability. But every one, Sen included, knew this. His result captures something about dynamics which was relevant at a time when Samuelson type 'turnpike theorems' had salience. His result had the heuristic effect of alerting researchers that 'single peakedness' couldn't restore legitimacy to 'turnpike' type thinking. Nor, before you start, can Muth Rationality. Think about it.
3) You use the word 'Acceptation' and grandly speak of 'Ackermann's Reflection Principle'. Why? What great insight into the foundations of Mathematics do you possess which is denied lesser mortals?

Why did you email this to me? Are you a masochist? Do you really think that a mere 'Academic' like me can attain the sublime heights of scatological abuse which you, the 'Poet of Socioproctology', have dedicated your life to?
I am sorry to disappoint you.

windwheel said...

Ha ha- made you look.
No, but seriously, I agree with everything you say about me- and btw I would have considered it my great good fortune, if not then then now, if I'd gone to 'Godhulia Gornmint College provided I'd had you as my lecturer. Instead, at the LSE, in 1979, I attended Sen's lectures on Social Choice and, a lasting testimony to my stupidity, thought he was as smart as he was arrogant. I was wrong.
You mention Lob's theorem and say Sen and everybody else was aware of its implications. This is not true. You say General Eqbm and Welfare Econ ain't univocal. This is silly and thoughtless because you go on to mention Samuelson's turnpikes. Fuck is wrong with you? Did you forget that I have access to Wikipedia? How about you use it once in a while yourself? Scratch that. Why not just use your brains?
Sen wrote before Sonnenschiem Debreu Mantel or Kirman & Koch etc. He didn't get- few did, ask Binmore- Arrow's Tarskian training and why brute Set Theory couldn't (precisely coz of stuff like Acceptation and Ackermann Reflection) rush into a topos where the angel of Relation Algebra feared to tread. Think for a second about Kripke's workaround for Tarski. What does it mean for Lob's 'modal fixed points'? Are you telling me Sen understood everything we now know about stuff like this back in 1970?
Are you mad or just stupid?
I actually look stuff up on the internet. I write poetry and poetry is about using your brain.
I emailed this to you because I'm a friendly guy. Suhrit praapti, is the condition for Yoga- Grothendieck or Patanjali.
Sen is a shithead. I'm stupid. Being stupid is poetic. Being a shithead is just such a fucking waste of a brain.
Far from disappointing me, you've made my day. Why? Because you've been honest with me.
Chimps fling their faeces at each other. That's how our species got our start. Starting with shit- Scatology as you learnedly term it- we proceeded to Sinn and Sin- Fregean Orbis Tertius Acceptation and its concomitant Third World of Strategic, or Spiritual, Dessication- but, dear fellow, Godhulia aint flinging faeces- it's the 'cow dust hour' when, Kazantzakis tells us, and old bard plucks his own throat's jews harp to renew once again Time's indefeasible Tiger melody.
We aint getting younger. Jus' sayin'.

windwheel said...

Oh and btw, of course Muth is relevant. Social Choice is a Co-ordination game. Think about it- Prude doesn't have a preference about who reads what, he has a preference about Rude's preferences and vice versa for the excellent reason that there is a big pay-off for a co-operative solution to a co-ordiantion (or dis-coordination) game which is too Pareto efficient.
Look, write to me separately or Skype and I'll go through things step by step.
God bless in any case.

windwheel said...

Or, alternatively, just carry on critiquing me here. I promise to deal with all points methodically and curb the 'poetic' stuff.
Anyway, great to hear from you.