Tuesday, 24 June 2014

Aumann agreement and Arjuna's Vishada

The Bhagvad Gita tackles Arjuna's Vishada (Depression) which arises when he realizes that by doing his duty as a warrior in the Kurukshetra War he will have ended up bringing about the worst possible outcome for all sides- including his own.
Previously, a Gandharva (demi-god) had granted Arjuna the gift of' 'chaksushi vidya' such that Arjuna could always visualize whatever he wanted to know, that too in the manner he wished to visualize it.

"The Gandharva said 'O Arjuna, I would like to impart to thee the power of (producing) illusions which Gandharvas alone have... This science is called Chakshushi. It was communicated by Manu unto Soma and by Soma unto Viswavasu, and lastly by Viswavasu unto me. Communicated by my preceptor, that science, having come unto me who am without energy, is gradually becoming fruitless. I have spoken to thee about its origin and transmission. Listen now to its power!rly One may see (by its aid) whatever one wisheth to see, and in whatever way he liketh (generally or particularly). One can acquire this science only after standing on one leg for six months. I shall however, communicate to thee this science without thyself being obliged to observe any rigid vow. O king, it is for this knowledge that we are superior to men. And as we are capable of seeing everything by spiritual sight, we are equal to the gods.'

Unlike Yuddhishtra, whose Vishada was only dispelled by having to learn Statistics and mathematical Game theory, Arjuna just gets, by 'moral luck', the equivalent of a perfect information, Bayesian predictor for everything. What's more, it has a neat little g.u.i such that it can show its results as a perfect simulation of a real world video, or even a Supernatural video, where Gods or Abstractions or  'Emergents' do the Narration, which is super-cool.

What has this to do with Aumann's agreement theorem? (which states that two people acting rationally (in a certain precise sense) and with common knowledge of each other's beliefs cannot agree to disagree. More specifically, if two people are genuine Bayesian rationalists with common priors, and if they each have common knowledge of their individual posteriors, then their posteriors must be equal.[1] Ziv Hellman has recently extended this result.)

Well, the Gita looks forward to a piquant situation where Arjuna fights his eldest brother, Karna, and slays him under the influence of 'Manyu' (dark anger).  Karna knows that if he reveals his birth, then Arjuna won't fight him and there will be no War. But Karna wants the War to go ahead- the condition for it is that 'common knowledge' is blocked by Karna's desire that his paternity remain unknown. It may be that Arjuna, who wants to obey his eldest brother, is constrained in some magical way by this wish of Karna. However, Arjuna- as is quite natural- does want to know the outcome of the War and immediately gets a vision of the horror and destruction and futility of it all. He still doesn't see the worst aspect of it for him personally- which is that he kills Karna in a mood of dark fury, exulting in revenge, and thus violates his own Dharma by committing the moral equivalent of parricide- but, perhaps, he doesn't want to see this because what he wants is already determined by Karna's desire that his paternity remain a secret and the War proceed as a great sacrifice by which warriors gain Heaven.

Interestingly, the Gita would still have the outcome if Arjuna had no special feeling of filial piety.Suppose Arjuna and Karna were not younger and older brother but two independent scholars of equal stature. Suppose both want 'common knowledge' except if at some later point they might regret it. Suppose, further that they each receive Arjuna's chaksushi vidya so they have zero computational or informational constraints. In that case, 'regret minimization' or 'Hannan consistency' militates for not Aumann agreement but disagreement iff the multiplicative weights index algorithm is efficient. Another way of saying the same thing is- Life is what makes the price of anarchy negative- or, as Heraclitus put it, Gods and Men die each others lives, live each others deaths.

Reading this interview with Hannan, what astonished me was how far ahead the Indians (mainly Bengalis and Maharashtrians) were in Statistics some seventy years ago. But, truth be told, there was nothing surprising at all about this.
The Indian clerisy- Revenue officials in the main- were doing boring Statistical Decision theory most of the time though, no doubt, with a bit of ars dictaminis Sycophancy as the cherry on top.

Thus, the traditional Indian reading of the Gita was always, au fond, Decision Theory based. It's basic finding- viz. Prescriptivity is vector not scalar- agree to disagree and then try to kill each other but stop short of complete genocide so some diversity at the margin is retained- is pretty much what Nature- the chrematistic aspect of Life- keeps telling us.

Since Hannan's result was known to the Indian Math/Stats community some sixty or seventy years ago and since, furthermore, Game theory was going from strength to strength over the same period, how come Maharashtrian Statisticians, like Kosambi, and Bengali Academics, like Amartya Sen, write utter shite about the Gita?

Well, clearly, it's because they are smarter than you and me- 'drunkards, fools and fishermen' that we are- because, though the Mahabharata was written for us, only the savants are blinded by it and proceed to enact their genocidal illusory wars coz Aumann agreement actually means not that you can't agree to disagree but that everybody has to just go on shitting all over everybody else lest, by some mischance, whatever strain of bacteria it is that makes our own farts pleasant to only our own nostrils go entirely extinct and it is to that great end that Poetry as Socioproctology too is a true emanation of the Blessed Gita.

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