Sunday, 1 May 2011

The Bhagvad Geeta and Binmore's Evolutionary Game Theory

This is Prof. Ken Binmore on the application of game theory to moral and political science. 'The most important result in this context is the folk theorem of repeated game theory, which roughly says that any stable outcome a society can achieve with the help of an external enforcement agency (like a King and his army, or God) can also be achieved without any external enforcement at all in a repeated game, provided the players are sufficiently patient and have no secrets from one another.  Game theorists take the view that a self-policing social system must be a Nash equilibrium in which each player is simultaneously making a best reply to the strategy choices of the other players. No single player then needs to be coerced, because he is already doing as well for himself as he can. We think that even authoritarian governments need to operate a Nash equilibrium in the repeated game of life played by the society they control if they are to be stable, because popes, kings, dictators, generals, judges, and the police themselves are all players in the game of life, and so cannot be treated as external enforcement agencies, but must be assigned roles that are compatible with their incentives just like the meanest citizen. In brief, the game theory answer to quis ipsos custodes custodiet is that we must all guard each other.
To this insight, my own work adds a game-theoretic approach to our understanding of fairness norms (Binmore [2005]). The folk theorem tells us that there are many efficient Nash equilibria in the repeated games of life played by human societies. This was true in particular of prehuman hunter-gatherer societies. Evolution therefore had an equilibrium selection problem to solve. The members of such a foraging society needed to coordinate on one of the many Nash equilibria in its game of life---but which one? I believe that our sense of fairness derives from evolution’s solution to this equilibrium selection problem. That is to say, metaphysics has nothing to do with fairness---if evolution had happened upon another solution to the equilibrium selection problem, we would be denouncing what we now call fair as unfair.
I go on to argue that our sense of fairness is like language in having a genetically determined deep structure that is common to the whole human race. I then give reasons why one should expect this deep structure to be captured by Rawls’ original position. The question then arises as to whether Rawls [1972] or Harsanyi [1977] are correct in their opposing analyses of rational bargaining in the original position. With the external enforcement assumed by both, the answer is that Harsanyi’s utilitarian conclusion is correct. Without external enforcement of any kind (so that there are no Rawlsian “strains of commitment” at all), I come up with something very close to Rawls’ egalitarian conclusion. That is to say, although Harsanyi’s analysis was better than Rawls’, but Rawls had the better intuition.
My analysis of our sense of fairness will doubtless be thought naïve by future scholars, but it is hard to conceive of a future approach that will not have a similar game-theoretic foundation.'

Evolutionary Game Theory of Prof. Binmore's sort is or was of more than evanescent interest, intersecting as it did with much hyped 'results' from Behavioural Economics and Primate Ethology and occurring in the visitor's lounge of Western Political Philosophy's Twilight Home as represented by the ludicrous lucubrations of shit-heads like Rawls and Nozick who did not understand that the concept of a contract- and hence the 'Social Contract'- differs from the concept of a relationship- or set of relationships constituting a Society- precisely by being a lottery and anti-social, purely for that reason, in direct proportion to its extent and degree of indefeasibility.

With our present chastened understanding of why systemic risk management amplifies catastrophic shocks, and how a credentialist crisis can make availability cascades so ubiquitous as to have all the appearance of a Revolution, all the more velvet for witless, with the end of 'the Great Moderation', not to speak of the the end of 'the end of History', the fundamental Kantian problematic re. demarcating heteronomy from an autonomy founded upon a reciprocal and fundamentally egalitarian Enlightenment-as-freedom has become suddenly more salient with the result that it is now the turn of the Whigs to find the idea of Evolution  unsettling.
This is because the empirical existence of polymorphism w.r.t (Kantian) reciprocal notions of morality and freedom raises the question of whether this is merely phenotypal- perhaps with environmental triggers, in which case ensuring a homogenous developmental ontogeny might re-establish an essential monomorphism, or else it is stochastic arising out of a mixed Evolutionarily Stable Strategy.
Moran (1992) has suggested that competition between kin millitates for this result as a way of 'hedging bets' so to speak.

The Whig theory of History can incorporate both the environmental trigger scenario - perhaps by invoking a mimetic to drive convergence of ontogenetic environments- as well as the mixed strategy theory- in the latter case by seeking to specify what that precise mixture might be and then concentrating on mechanism design such that it bestows prescriptivity on its own project.
The alternative- viz. to admit genetic polymorphism as responsible for innate differences in notions of morality and, its Kantian reciprocal, freedom  - forces Whiggery to cash out as either a hierarchical special-pleading or else a nihilsm or panalethia. Which, being au fond a De Maistrean theory of sacrifice, Whiggery can live with because only its vitality of life, not its virulence of legitimacy, is lost thereby.
Consider this eloquent extract from the Sage of Konisberg's  'Differences in National characteristics, so far as they depend on the distinct feeling of the Beautiful and Sublime'
'A despairing man is always a strict master over anyone weaker, just as with us that man is always a tyrant in the kitchen who outside his own house hardly dares to look anyone in the face.  Of course, Father Labat reports that a Negro carpenter, whom he reproached for haughty treatment toward his wives, answered: "You whites are indeed fools, for first you make great concessions to your wives, and afterward you complain when they drive you mad."  And it might be that there were something in this which perhaps deserved to be considered; but in short, this fellow was quite black from head to foot, a clear proof that what he said was stupid.'
Rawls, speaking of the difference principle (by which only those departures from equality of outcome are permitted which benefit the worst off), points out that 'least advantaged' is not a (Kripke) rigid designator always picking out, say, women rather than men, whites rather than blacks, British rather than Indians, across all possible worlds. However, the elementary theory of price and service provision discrimination explains how the difference principle militates for racism and sexism because these are cheap ways to segment the market (i.e. they are barriers that are very costly to get around but very cheap to enforce) such that a good or service with very high fixed costs which might not otherwise be provided becomes available. In other words, in deciding who to listen to, who gets 'voice'- 'loyalty' and 'exit' (Hirschman)- Rawls's Kantianism is always gonna be saying stuff like 'the fellow was quite black from head to foot, a clear proof that what he said was stupid', unless this involves a risk of having the shit kicked out of you, in which case the safest thing is to pretend you're a Mathematical Economist or Post Modern or incarnate some other such oxymoron.

Before embracing so odious an outcome, and bearing in mind Moran's suggestion that kin rivalry might catalyse a stochastic polymorphism- such that kin-folk with different conceptions of morality clash to the extent of violating Hamilton's rule- the Indian Mahabharata, an early Iron Age Epic redacted in the Axial Age, might be worth examining as it deals with an epoch changing war between cousins- as trivial in conception and catastrophic in its consequences as the Kaiser's War and the further conflagrations to which it gave rise. Moreover, the Mhb makes explicit mention of Probability and Game Theory as being sciences that need to be mastered for a man, already of the highest moral and empathic character,  to rise above heteronomy and rule as a Just King.  Another, related Epic, the Ramayana, deals with a King of an even higher type whose 'Ramrajya' (rule of King Rama) dispenses, at least in its idealized form, even with Rawlsian 'strains of commitment'- i.e. a pre-existing  internalized consensus or set of norms- instead relying upon the agent with greater autonomy to always choose such that the more heteronomous agent's choices are valorized in a manner intended to effect the up-liftment of the latter.

The Indian Mahabharata, is an artificial environment where all agents and interactions have a dual such that the entire corpus conserves, as if by Noether's theorem, karma  and dharma- the first of which relates to the manner in which, under repeated games, coalition membership (caste status) as well as stochastic shocks are  serially determined such that the agent's preferences and outcomes change radically in each birth. The second notion, dharma- duty or religion has to do with correct conduct, entitlements and obligations as well as notions of fairness and just proceeding which can either be agent or coalition specific or 'paro dharma' (higher righteousness) i.e Universal and context free.

The Bhagvad Gita is a chapter within the Mahabharata dealing with the theophany of Lord Vishnu to Prince Arjuna in the context of the latter's 'vishada' (mental depression, aboulie). The dual of Vishnu's theophany in the Gita, is that of Lord Shiva in the episode known as the Kiratarjuniya. Briefly, in the latter, Lord Shiva, in the form of a tribal chief, disputes with Arjuna the question of whose arrow actually felled a boar and the issue is resolved by main force. Shiva is more powerful than Arjuna and able to seize his Gandiva bow. Arjuna realizes this is the Supreme Lord and seeks his blessing.  The Gita deals with the opposite situation. Here the Supreme Lord, in the form of Lord Krishna, seeks to persuade Arjuna that any arrow that he lets fly at his enemies (including those directed at his eldest brother, Karna, to whom, if Karna choose to make his true parentage known, Arjuna would owe a duty of obedience) do not actually slay anything. All are slain by the Lord alone. In other words, both Shiva and Krishna are telling Arjuna the same thing- neither the guilt nor the reward of his arrow's hitting the mark belong to him- but the methods used are different. Shiva succeeds by besting the warrior prince in a physical fight- something Arjuna can immediately grasp. Krishna however delivers a long philosophical discourse- this is the substance of the Geeta- and it is not clear that Arjuna really retains anything of it in his head.

How does Game Theory come into this?

Well, by the MhB's system of symmetries, if Arjuna's vishada (depression) is addressed than somewhere else, someone else's vishada must be addressed. Whose? And where?

The first thing we might note, in seeking an answer to this, is that Arjuna's 'dual' appears to be Karna. The pathos of the Geeta is that Arjuna senses that he is about to commit a terrible crime in fighting his kinsfolk. He does not know that Karna is his eldest brother and that by killing him he will commit a sin equal to parricide. Krishna is in a difficult position. His message in the Geeta is 'act dispassionately', yet he will himself egg on Arjuna, by awaking his manyu (dark anger or sense of grievance) to kill Karna in an unsporting manner.

By the Mahabharata's system of symmetries- its 'double entry book-keeping heuristic' so to speak- if Krishna eggs on Arjuna to kill Karna by awaking his dark anger, then there should be another episode where Arjuna, in wrath, seeks to slay the person he thinks is his eldest brother-viz. King Yuddhishtra. In that episode Krishna gets Arjuna to redirect his wrath into words- Krishna tells Arjuna to utter a condign criticism of his elder brother, for to humiliate a man is to inflict a sort of 'Social death' upon him. Arjuna does this so as not to break his vow (to seek to kill the one who demands he surrender his emblematic Gandiva bow) but then feels so wretched he wants to kill himself. Krishna tells him that dharma is subtle, none understand it, the correct thing to do now is to utter an accurate description of one's own great merits- for to praise oneself, or show one's true greatness, is to slay oneself. Arjuna complies. After this, he humbly begs forgiveness from King Yuddhishtra and persuades him to continue to rule over the fortunes of their house.

The important point here- perhaps too obvious to be spelled out- is that Krishna's theophany in the Geeta was a type of self-slaying, a Christ-like sacrifice, for the purpose of assuring his devotees that the Lord takes on the sins of his devotees and pays the price for them. From the point of view of Faith, this is the meaning of the Geeta. Game theory, mechanism design, the evolution of notions of fairness and Justice and their application to the sort of Social Order we might choose behind a Rawlsian veil of ignorance and other such secular considerations appear to have no importance to reading the Geeta.

If, lacking Faith, we nevertheless persist, seeking to read the Geeta with the aid of its dual, the Kiratarjunia,  we find that dharma is indeed subtle, as Krishna says, and beyond the ken of Faith alone.
Why is this? Well, in both texts, Arjuna is bested by a sort of 'shock and awe' that God commands. Yet, taken together, both texts serve to whip up thymotic rage for an inhuman purpose. Shiva, in essence, challenges Arjuna to a fight by enraging him. The Destroyer God normally grants a boon to an ascetic not for the purpose of making him puissant above all others but, by giving full reign to his egotism or hubris, to cause the ascetic to destroy himself by a heinous transgression which Vishnu (the Preserver God's) avatar will punish. However, in the Kiratarjunia this motif is reversed. Shiva distracts Arjuna from his austerities by provoking him to a fight. The boon he grants does not destroy Arjuna himself but is part of a wider plan to   greatly decimate the entire warrior class to which Arjuna belonged. Similarly, the Geeta, despite all its fine philosophy, serves the purpose of bringing about Arjuna's killing of his eldest brother while in a state of dark anger. In other words, both tell us only about heteronomous conceptions of dharma- actions required of a mortal for purposes beyond his ken.

In contrast, a quite different tack is taken in the portion of the MhB which deals with the vishada of King Yuddhishtra- who as the head of his house is a principal rather than an agent- and who is the incarnation of 'Dharma' (Righteousness).

Yuddhistra is something approaching the ideal moral being. Previously, he had been given the choice of saving the life of one of his brothers. Instead of choosing the strongest or the most able, he chose one who had a different mother so that both maternal lineages might be preserved. This, by itself, throws a light upon Harsanyi's 'rule utilitarianism' notion that ethical decisions require a sort of impersonality such as would arise from not knowing in whose shoes one might find oneself.  Yet, one already fills a certain pair of shoes and can't envisage a Universe in which that particular view point is not valorized. There is a sort of Anthropic principle at work here or, at the level of probability distributions, a Monty Hall type Problem. Impersonality can't be truly self-abnegating, at least not consistently, otherwise no calculus could be derived.

Can impartiality of this type be truly ethical if it forecloses the option of self-abnegation?
Yes, if 'fairness' is vector, not scalar- if, as Binmore says, it is structured like a language, then it is a necessarily a Bakhtinian heteroglossia- referencing a set of compossible evolutionary stable strategies.
However, there is a sort of Newcombe's problem type situation here which also inheres in the Kantian categorical imperative. Referencing Nozick's- 'Judge Hercules' who can always re-interpret in a harmonious manner the whole body of the Law such that it's fabric suffers no tear of wrinkle- we might say that we would always want our choice to have this quality. But to seek to conform to the prediction of Newcombe's oracle or Judge Hercules's ruling in the Court of the Kantian Categorical Imperative- even absent any factor militating for heteronomy- is nevertheless to feel a curb placed upon one's free will. The poisoned chalice placed before us which, as with Kavka's toxin, we drain so 'Thy Will, Lord, not mine, be done' turns out to be the only way to evade the death sentence of heteronomy.

Returning to Yuddhishtra deciding which one of his brothers to revive- if he is to be impartial, surely he should toss a coin, after all, each of his brothers has an equal right to live and ought to command an equal portion of his love. In particular, to ordain of a pair of twins that one should live to mourn the other, appears the opposite of rule-utilitarian 'impersonality' in that, it may be, this maximizes the bereavement for the survivors while simultaneously minimizing the fighting ability of the depleted band of brothers. No doubt the Just King will derive a sense of inflated pride by this deliberate choosing of the worst possible outcome, but what of the other brother? Suppose it is easier for Yuddhishtra to make tough 'ethical' decisions of this sort than it would be for the other. Suppose further that the survivor of the (presumably identical) twins, by reason of Hamilton's rule (kin selection), knows that Yuddhistra's gift to him of his life would not be one who could have as easily reciprocated- then the Just King's fairness ethic is not symmetric and thus all the more unfair.

Survivor's guilt has been maximised merely so an insufferable prig can plume himself.  In other words Yuddhishtra has made a decision for the group which is not a canonical solution to the co-ordination problem here- viz. what choice would be 'natural' and thus cause the least resentment as being what any of the other guys would have done had they had to choose. It appears, hence, that the Just King makes the worst possible decision but since, in this instance, the game was 'loser takes all', purely by chance, Yuddhishtra gets back all his brothers.

This King is depicted as having one besetting vice- gambling fever. His elder brother, Karna, is unreasonably generous- but it is a noble fault. Not once, but twice (because everything in the MhB happens twice), Yudhhishtra gambles everything away- including himself, his brothers and their common wife.

The fact that the gambler Yuddhishtra is described as the incarnation of Dharma even before he learns Probability and Game Theory, thus becoming an expert gambler, has puzzled Indian readers.

True, this may be seen as simple 'hamartia' (the tragic flaw in an otherwise noble personality which makes for good drama) or it may be that in a hierarchical Society where slavery exists it is only fair that the King and his beloved brothers and wife (with whom he shares everything) take their turn at the hazard of ending up at the bottom of the heap. As Binmore points out, Rawls and Harsanyi arrive at opposite conclusions as to what will happen from behind the veil of ignorance based on the constraints they place on the preferences of the idealized rational agents assumed for the exercise.

Yet, if Yuddhishtra is truly rational, the question arises as to why he does not abandon Caste based Dharma for something like Moh Tzu's mix of pragmatic utilitarianism coupled with a Creedal deontology of Universal Love?

Perhaps, belief in the karma theory precludes this outcome.  Lifting all constraints on preferences and world-views behind the Rawlsian veil, however, has the result that no way remains to rule out in advance that what will ultimately be chosen is not Borges's 'Lottery in Babylon'- where anything can happen to anybody. Indeed, if the agents believe in metempsychosis, Borges's Lottery dominates all other solutions!

However, those theodicies or spiritual traditions which have embraced this outcome sooner or later explicity come out and say that both karma (metempsychosis) and dharma (righteousness) are empty and have no ontological significance.

Indeed, the problem with the doctrine of God as the sole efficient cause is that it tends to render the Godhead an irrelevance from the human point of view. Fatalism of this sort cashes out as thymotic hedonism. If only our emotions are ours, not our actions, indulge them to your heart's content!

Ghazali's occassionalism puts the Ghazal universe on precisely this insane trajectory. The notion that emotions- as Darwinian algorithms of the limbic system- have evolved because of their adaptiveness in decision making, signaling, preference revelation and so on is thrown out of the window. No Society could last very long embracing such a doctrine.

Yuddhishtra's vishada (depression) arises in the following manner. He feels compelled to agree to every game of dice to which he is challenged. Since the other side have a skilled gamester on their team, Yuddhishtra always loses. Yet he firmly believes he and his brothers should be given something- even a small share- of the ancestral patrimony. He is prepared to fight and shed blood to maintain his rights in this respect. But, as his brother Bhima warns, what is the point of his winning back their share of the Kingdom if he just dices it away again? Bhima is duty bound to obey his elder brother but, since it appears that his elder brother has an addiction and thus lacks competency, Bhima proposes to kill of all the enemies himself and then crown Yuddhisthra, taking all the guilt for so doing upon himself.
However, this itself is a departure from the path of righteousness. Yuddhistra is caught in a double bind. His hamartia is the source of his heteronomy. Fortunately, just as Arjuna's Vishada is dispelled by a divine discourse, so too is Yuddhishtra's. He hears the story of Nala and learns probability and Game theory. Now he needn't fear losing everything to a dice game. Furthermore, he has also learned that the seemingly immutable caste hierarchy of ancient India has no moral or soteriological significance and can be dispensed with.

If the Geeta is read without keeping this episode in mind, the result would be a valorization of a hierarchical, misogynistic society in which duty involves killing even kinfolk without mercy. The great mathematician Andre Weil, perhaps because he subconsciously grasped the system of symmetries underlying the Geeta, rejected such a view. The plain reading, for him, as for his colleague, the Gandhian, Vijayraghavan, was do your own duty- i.e. what you want- rather than what others demand. This too was a misreading. Weil tried to dodge the draft- maths was his duty not manning a machine gun- but, by that very step, almost lost his life.

The MhB is about the self destructive collapse of one sort of social order- the heroic age where thymos ruled supreme- and the dawn of another more mercantile and rights based social order- where heteronomy spelled backwardness and internecine bloodshed, while intersubjective autonomy and rationality pointed the way forward to a great advance in material civilization.

However, it remains an open problem, for me at any rate, as to whether the light that Game Theory throws upon the Geeta is not reflected back upon it as an exercise in futility as damning as the Just King's other great strategic blunder viz. his victory at Kurukshetra where, once again, it was a case of loser takes all.


  1. I don't understand this. You write-
    'Rawls, speaking of the difference principle (by which only those departures from equality of outcome are permitted which benefit the worst off), points out that 'least advantaged' is not a (Kripke) rigid designator always picking out, say, women rather than men, whites rather than blacks, British rather than Indians, across all possible worlds. However, the elementary theory of price and service provision discrimination explains how the difference principle militates for racism and sexism because these are cheap ways to segment the market (i.e. they are barriers that are very costly to get around but very cheap to enforce) such that a good or service with very high fixed costs which might not otherwise be provided becomes available. In other words, in deciding who to listen to, who gets 'voice'- 'loyalty' and 'exit' (Hirschman)- Rawls's Kantianism is always gonna be saying stuff like 'the fellow was quite black from head to foot, a clear proof that what he said was stupid', unless this involves a risk of having the shit kicked out of you, in which case the safest thing is to pretend you're a Mathematical Economist or Post Modern or incarnate some other such oxymoron.'

    What is the point you're trying to make and how does Kripke 'rigid designation' come into it?
    Rawls, especially in his later, more Leftist, work does not endorse racism or sexism. The whole point of the 'veil of innocence' is that you don't know in advance whether you'd be a woman or a member of a minority. Therefore, you will choose a social order such that, if the worst comes to the worst, you will have a bearable existence though belonging to the least advantaged in society.

  2. Rawls is an 'ideal theory'. Yet it imagines an 'original position' such that agents, though knowing nothing of what gender role or position in society they will be assigned, do know of 'certain fundamental interests they all have, plus general facts about psychology, economics, biology, and other social and natural sciences. The parties in the original position are presented with a list of the main conceptions of justice drawn from the tradition of social and political philosophy, and are assigned the task of choosing from among these alternatives the conception of justice that best advances their interests in establishing conditions that enable them to effectively pursue their final ends and fundamental interests.'
    The problem here is the 'facts' and menu options they are offered arise out of a sort of Knowledge as a Public Good. What sort of Knowledge? Well, it deals with 'certain general facts about economics, psychology and so on'. These facts don't exist in an unproblematic manner. They are in joint-supply with something else viz. the policing or market segmentation arising out of the provision of this Public Good.
    There is an extensive literature on how Society can pay for Public Goods (which are non-rival and non-excludable as in the case of the 'general facts' and menu of options agents in the original position are faced with). One of the general facts about Econ is stuff to do with price and service provision discrimination permitting the raising of enough revenue to cover the provision of something with high fixed costs which wouldn't otherwise exist. The cheapest way to segment markets is along lines which are costly to evade but cheap to enforce. Obvious differences, e.g. of gender or color or language or religion etc will tend to be used. In other words institutionalised discrimination is bound to occur. True, agents in the original position don't know what will they will be. But, if they are doing something morally more worthwhile then just taking a gamble- playing a sort of Social Russian roulette- then the menu they are presented with 'of list of the main conceptions of justice drawn from the tradition of social and political philosophy' must include conceptions of 'dynamic' justice which permit the amelioration of institutional discrimination by some parallel reparative process. Even if Rawls 'ideal theory' deals only with an economy which lasts for one second and thus has no dynamics, the agents choice situation in the original position involves a dynamics- viz. comparison of different conceptions of justice from the Menu and a rational calculus based on applying the 'general facts of Econ, psychology etc.' To argue otherwise, viz. that this decision making process has no dynamics is to say facts and conceptions can be cognized and reflected on in a manner that renders the entire history and practice of Philosophy, of Economics, of Psychology, etc, utterly and entirely beside the mark. This is an extreme assumption Hitler, purging 'Jewish Science' and 'African Music' and so on, is generally considered a bit of an extremist. Still, to concede your point, Hitler's methods might ensure that no dynamic conception of Justice, or inconvenient facts about Econ, or Psy etc, get presented to those lucky lucky people placed in Rawls's original position.
    You mention 'rigid designation'. In this context, it looks as though Rawls is offering agents a real choice from across possible worlds. But choice, like cooking, or making love, is something we learn how to do by doing more and more of- that too in an inherently dynamic context.
    'Ideal theory' is just bad rhetoric and slip-shod thinking. So, too, is everything else.
    Except South Park.