Occasional reflections on Life, the World, and Mathematics

The president’s dilemma


In the classic prisoners’ dilemma, two members of a criminal gang have been caught by police. There is enough evidence to convict them of minor crimes, but without testimony from one of them they will receive only a light sentence, say one year in prison. If one of them agrees to cooperate with the investigation, prosecutors will let him out for time served, and be able to send the other to prison for ten years. But if they both cooperate with the investigation, both will go to prison for five years (perhaps because the prosecutors will have their information, but not their testimony). Key to the game is that the players are unable to coordinate their strategy. Clearly the best for both of them would be to keep quiet, but the strategy of cooperating with the investigation is superior, from their private perspective, regardless of what the other player does. So they both talk, and both get heavy sentences.

One weird thing about the story here is that the symmetry really doesn’t make sense. It’s not impossible, but it’s peculiar to imagine prosecutors being so interested in pinning the major crime on someone that they’re willing to let a confederate walk free, but indifferent to who flips on whom. That suggests we consider a less-known hierarchical version of this game, where one player is the powerful boss of a crime syndicate — let’s call him “The President” — and the other one is “The Attorney”, who knows all the details of his crimes, and is sufficiently involved to be criminally liable himself. Let’s call this game “The President’s Dilemma”. In this version, The Attorney has been arrested, but could buy his freedom — or a lighter sentence — by testifying against the President. Or he could keep quiet. The President’s options are to pardon or not to pardon. The pardon has to come at the appropriate time, so it can’t be issued right up front. So each one needs to make a decision, and it seems they can’t avoid ending up in the worst state, where The Attornay testifies and The President doesn’t pardon him. they can’t communicate about it. Or can they?

The President can take actions that signal to the Attorney that he intends to signal concern with his plight, and hence intends ultimately to pardon him. The problem is, too blatant actions could aggravate The President’s obstruction-of-justice problem. So it has to be subtle, the kind of action The President would take anyway, but which would have a special meaning for The Attorney. Something like hiring a legal expert to assist The President, who has special connections to the prosecutors who are threatening The Attorney.

But what if the message is too subtle, and The Attorney doesn’t understand it? If only there were someone at arms length from the President who could interpret this signal in plain language. Someone like…

Aren’t we lucky to have civic-minded independent experts like Alan Dershowitz to tell the “public” what it needs to know?

It’s striking, as many have commented, that even Donald Trump’s defenders — of whom Dershowitz is certainly one of the most savvy — have given up any pretense of believing that Trump is an upstanding businessman, perhaps fallen in with some dodgy associates, whose interests would be best served by getting everything out into the open so it can be cleared up once and for all.

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