One of the least fruitful dead-ends in any online discussion forum is the Eternally Refined Analogy.
Someone attempts to illustrate their argument with an analogy which, being only an analogy, is not perfectly equivalent to the gist of what they're trying to say. And with startling speed, the original matter of the argument is abandoned and the conversation becomes primarily about criticism and refinement of the analogy.
Part of the reason I've never been particularly fascinated with game theory is that it reminds me of this phenomenon. It seems a bit too much like one big round of the Eternally Refined Analogy.
I appreciate it's potential contributions to all sorts of things — computer programming, economics, diplomacy, etc. — but it's always struck me as having an even greater potential to become the analogy that distracts us from the thing itself.
Having said all that, I was still fascinated by the lively and surprisingly accessible discussion of game theory and the prisoner's dilemma in a recent series of posts by Brad DeLong — starting here and continuing here, here and here. (Part of what made this particularly interesting for me is that, while obviously very familiar with the subject, DeLong doesn't seem overly impressed with its usefulness either.)
This isn't something I studied in grad school. I spent those years serving the Queen of the Sciences, and theology hasn't warmed up to game theory. (From what I've read of the Summa, though, I'd bet Thomas Aquinas would've loved it).
It's difficult for theologians to hear the intricately refined scenarios posed by game theorists without hearing the unspoken preface, "And behold, a certain lawyer stood up, and tempted him." So if presented with something like the prisoner's dilemma, a theologian is likely to respond with something like, "A certain man went down from Jerusalem to Jericho, and fell among thieves …"
But, unlike Jesus, I'm going to try to provide a straight answer here and describe three different theological objections to the prisoner's dilemma.
1. You have heard it said a tit for a tat, but I say to you …
The prisoner's dilemma purports to present a complex scenario involving you and one other actor. But Christian ethics involving only you and one other actor are not complex. Astonishingly demanding, but not at all complex. In such scenarios, Christ's sacrificial ethic seems unambiguous. Always cooperate; turn the other cheek, walk another mile and let him have your cloak as well. This seems a bit insane — that sort of behavior could get you killed, crucified even — and seems an extraordinary test of courage, but it's not really much of an inetellectual conundrum.
This imposed definition of rationality seems necessary to preserve the game from the subversive Christ-types, but the game cannot withstand such presuppositions either: if the game's purported aim is to determine what is rational, it can't very well start off saying it will allow only one possible answer. DeLong makes this very point here:
If you set up as an axiom of rationality that a rational, logical agent must always choose to play a dominant over a dominated strategy — well, Grasshopper, you have begged the question, and you have to answer the next order question: why you think that your rational, logical agents are smart?
So either way, in a sense, the very possibility of renunciation and altruism subverts and shatters the world of the game. (This, by the way, is much closer to the actual meaning of John's Apocalypse than anything ever dreamed of by our friends LaHaye and Jenkins.) It's a bit like the Harrowing of Hell, in which the willing loser sets all the other prisoners free.
(In the real world, of course, scenarios involving and affecting two and only two actors are so rare as to be virtually nonexistent. So conclusions drawn from either the basic prisoner's dilemma or the basic self-abnegating ethic of the Sermon on the Mount are not likely to be immediately applicable to most real-world scenarios. Both models can be expanded to accommodate more complex realities involving multiple actors. For a good discussion of the latter case, I'd recommend Reinhold Niebuhr's Moral Man and Immoral Society.)
2. Don't hate the player. Hate the game.
Let me clarify one point above. I wrote that, "The prisoner's dilemma purports to present a complex scenario involving you and one other actor." The actual scenario involves at least a third actor, and probably many more.
Every prison has a warden and guards, within and without. Just who is the evil bastard running this warped hypothetical Gitmo?
That's not the point of the game, I'm told, but how can it not be? How can that question not be the single most important point of the game? If you are a prisoner and you think it matters whether or not you pursue a "dominant" strategy towards the other prisoners then you have already surrendered in the only game that really matters. In that game, all the prisoners are on one side and the warden is on the other.
To put this in more theological terms, the scenario denies the possibility of two things which are non-negotiable: solidarity and liberation. Solidarity requires that you refuse to be pitted against your fellow prisoners. Liberation demands rescue from the hand of the oppressor.
Our text here is not the Sermon on the Mount, but all of the prophets from Moses through John the Baptist and Jesus himself. If this were a scenario of only two — just you and the warden — then "let him have your cloak as well" might apply. But the warden hasn't only taken your tunic, he is also oppressing Prisoner B and who knows how many others.
This seems more like an appropriate time to make a whip out of cords, kick over some tables, set the oppressed free and break every yoke.
3. A little lower than the angels
If you tell people you're studying theology, they tend to think you're mainly studying the nature of God. But theology is just as much the study of human nature. And while theology students consider these subjects inextricably intertwined, the latter study tends to be a bit richer and less speculative since human nature is so much easier to observe.
The strange creatures described as the actors in the prisoner's dilemma do not seem compatible with the Christian understanding of human nature. They scarcely seem recognizable as humans at all. Here is a sentence from Brad DeLong's summary of the requirements of a typical prisoner's dilemma scenario:
Each is a self-interested being, caring only about his or her own payoffs — they are neither altruistic nor envious.
The first assertion presumes a great deal about not just human nature, but about the way the world works. It presumes that it is possible to be "self-interested" without regard for the well-being of others. If that were truly a possibility, and if it were also true, as DeLong goes on to say, that "each is a logical being understanding the structure of the game," then these prisoners would have only one goal: To supplant the warden. Super-men shouldn't be content to sit in their cells, plotting against their fellow prisoners.
Christian theology regards the first half of this sentence as a contradiction. Your own self-interest requires you to care about more than your own payoffs. We are our brothers' and sisters' keepers. These prisoners bear the mark of Cain — by refusing to be their brother's keeper, they end up having no keepers themselves, and no brothers or sisters. Such restless wandering is more than we can bear. It is, in a word, inhuman.
This perspective on human nature is hardly unique to the discipline of theology. Psychiatry has its own vocabulary to describe people who only care about their own payoffs. The DSM IV calls them "sociopaths."
I can't find a toehold for humanity in the second half of that sentence either — "they are neither altruistic nor envious." Humans, of course, are both. I could cite Augustine here, but you don't need me to, since you've likely known enough humans to agree with that description regardless of whether or not it's "Augustinian."
The usual error is to pretend that we humans are exclusively one or the other — altruistic or envious. The problem here with the prisoner's dilemma — pretending that we can be neither, yet still be recognizably human — is novel, but still an error.
(Image via the British Library from a mid-14th-century Book of Hours.)
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