Karma Dilemma

In “Nice Guys Finish First”, the penultimate chapter of The Selfish Gene, Richard Dawkins digresses into game theory to explain the evolution of co-operation. The centerpiece is a simple game called the Prisoner’s Dilemma. The one-shot version of PD is straightforward: the rational move for any player is to always defect. The Iterated Prisoner’s Dilemma or IPD, where players face each other in multiple rounds, is much more interesting, because co-operation emerges as a viable strategy. “As a biologist”, Dawkins says, “I agree with Axelrod and Hamilton that many wild animals and plants are engaged in ceaseless games of Prisoner’s Dilemma, played out in evolutionary time.”

You can read the gory details in Wikipedia, but my eye was caught by this particular notion:

But none of this works unless the game is iterated. The players must know that the present game is not the last one between them. In Axelrod’s haunting phrase, the ‘shadow of the future’ must be long. But how long must it be? It can’t be infinitely long.

From a theoretical point of view, it doesn’t matter how long the game is; the important thing is that neither player should know that the game is coming to an end.

But it can be infinitely long! The Hindu-Buddhist doctrine of karma and reincarnation provides an almost mathematically ideal playing field for IPD.

  1. The universe keeps score.
  2. The game is infinite, and your karma score is rolled over to your next billing cycle on death and reincarnation. Some of your karma points may be redeemed towards determining your next birth-form. Players believe that the game is not limited to this lifetime, and this increases their tendency to play co-operate rather than defect.

Since the universe keeps score and deals out retribution, players find it less necessary to get caught up in rounds of mutual retaliation. Of course, this biases strategies perhaps a tad too much towards Sucker, with the usual failure mode of being invaded by Cheaters. As a neat side effect, the doctrine also “explains” unjustified success and suffering as the result of account balance brought forward from previous births.

In a tribal society, where everyone knows everyone else, the tribe itself can keep score. Since most transactions occur between members of the tribe, and all tribe members realize that they will be playing again and again, a karmic structure appears superfluous. Older members who are about to exit the stage are the ones in most danger of getting defected against. According to Steven Pinker, this probably stimulated the development of ancestor worship.

Ancestor worship must be an appealing idea to people who are about to become ancestors. As one’s days dwindle, life begins to shift from an iterative prisoner’s dilemma, in which defection can be punished and cooperation rewarded, to a one-shot prisoner’s dilemma, in which enforcement is impossible. If you can convince your children that your soul will live on and watch over their affairs, they are less emboldened to defect while you are alive.

In larger agglomerations, like urban areas, where most transactions are one-shot interactions between strangers, there is a tendency for defect to prevail. It’s interesting to speculate that the rise of the doctrine of karma and reincarnation was part of a self-reinforcing “virtuous circle” with the rise of post-agricultural civilization.

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2 responses to “Karma Dilemma

  1. that’s actually a very clever and tight analogy. to make it more precise, I’d say your probability of defecting depends on your expectation that the current iteration is the last one. one way to model this is to basically use NPV analysis, where your discounting of the future represents the risk that the future might not happen, and you can actually use the sort of ‘do a discounted integration of future moves’ thing to show that tit-for-tat is optimal in an ESS sense.

    there is a similar probability thing in karma — recall Pascal’s clever computation, where he said even if there is only a small probability of god/heaven/hell being true, it pays to be religious because the upside/downside are so extreme compared to the neutral outcome of atheism.

    so i think your argument can actually be made completely mathematical. what is the probability that grandpa will come back and haunt me as a ghost? or as a snake in next-life that bites me? if it is non-zero in a bayesian sense, it makes sense to do ancestor worship, take care of elders etc.

  2. Indeed. Further down the chapter,

    … in real life it is often possible to make a statistical guess as to how much longer the game is likely to last. This assessment may become an important part of strategy…

    … Each player can be expected to behave as if he possessed a continuously updated estimate of how long the game is likely to go on. The longer his estimate, the more he will play according to the mathematician’s expectations for the true iterated game: in other words, the nicer, more forgiving, less envious he will be. The shorter his estimate of the future of the game, the more he will be inclined to play according to the mathematician’s expectations for the one-off game: the nastier, and less forgiving will he be.

    Karma plays out in the same medium again and again – like a pawn which marches off the end of the board and re-emerges, perhaps in a different form, back at square one of the same game. Contrast this with other theologies in which a pawn goes off the “Earth” board to a different game forever. The Pascal argument surfaces, and given the infinity of time you are expected to spend in the afterlife, it pays to optimize your chances for the one-shot decision point which determines whether you score a harp or a red-hot trident up the backside for the rest of forever. For expansionist reasons, many religions have an amnesty scheme where all you need to do is sign on the dotted line of sincere belief and repentance and any negative score you have accumulated is reset, plus you get a ticket to harpdom. A smart player can defect for most of his duration on the earth board, gaining hugely in “material” score, and signing up for the Prodigal Son program just before he’s due to exit to the next board.

    One of these schemes has an elegance born of simplicity and symmetry, and leads to “good” behaviour. The other can lead to highly defective behaviour against fellow humans – some of it religiously endorsed – without diminishing anticipation of the eternal raisin-filled desserts of paradise.

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