According to Game Theory, the Senate Is Already Lost

The Republicans’ refusal to play by the rules has assured mutual, nuclear destruction. The only thing left is forgiveness.

The Senate is at a crossroads over the Gorsuch nomination.

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Judge Neil Gorsuch’s Supreme Court nomination will come up for a vote in front of the Senate on Friday, and the results may be momentous. The Democrats are planning to filibuster, which will likely prompt the Republicans to change Senate rules to no longer require a 60-vote majority for Supreme Court nominations. [Update, 2 p.m.: They did.] This is something no one really wants. As Jim Newell wrote in Slate on Monday, “Very few members of the Senate, on either side, are happy right now.”

All of this, from the Merrick Garland antics to the filibuster to the filibuster killing, seems like an awful tit-for-tat kind of playground dynamics, except one with much, much higher stakes. So why are our elected officials engaging in it?

Perhaps because tit for tat has sound game theoretic rationale.

The most famous example in game theory is the so-called prisoner’s dilemma. In this situation, criminal co-conspirators are brought in and questioned separately about their roles in a crime. They know beforehand that if they both stay silent (“cooperating” with each other), their sentences will be much lighter than if they both rat out the other (“defecting”). The complication is that if you rat out your friend while he continues to cooperate, then you get a further reduction in your sentence. Given that both would receive the same better reduction, the “rational” thing to do is for both to rat out each other, even though it is a less than best (“suboptimal”) outcome.

As described, the prisoner’s dilemma is a one-shot deal. But if you play a one-shot game repeatedly, eventually you can build a strategy that allows for learning, bluffing, and retaliation. Repeated games turn out to be very complicated to understand mathematically—a good deal of insight into them has been generated by simulations, both computer and human. The most famous example of the latter was a “tournament” run by the University of Michigan social scientist Robert Axelrod in 1980. Axelrod invited game theorists and social scientists to repeatedly play prisoner’s dilemma games against each other; in some cases the game incorporated memory of their previous plays and the plays of their opponents and the outcomes of these games. The “agents” were all self-interested and had only the goal of accumulating the highest overall score—or in prisoner’s dilemma world, the smallest accumulated prison time.

Surprisingly, the winning strategy in Axelrod’s tournament was a simple one, known to children all around the world: tit for tat, submitted by Axelrod’s former Michigan colleague, Anatol Rapoport. The strategy is basic: You cooperate in your first game, but after that, you simply look to see what your opponent did last time, and then you do that in this next game. If in the last game he or she defected, then in this game you defect. If in the last game he or she cooperated, then in this game, you cooperate. And most of the time, when using this strategy, you win.

So the Democrats have math on their side as they roll out the filibuster. The intransigence of the Republicans should be met with intransigence—at least from a theoretical point of view. But then what? Well, there is a choice—a new candidate could be proposed, providing a new chance for cooperation and defection on the important issue of the Supreme Court nomination.

Or, they can change the game. And that seems like what they’re going to do: Change the rules of the Senate. Voting down party lines will give the Republicans a double “win,” as it will rewrite the rules of the Senate and usher in their choice of Supreme Court justice. Of course, this double win might only be sustained while the Republicans are in charge, but the current political climate seems to have voters and lawmakers much more interested in winning than in preserving norms. And more critically, “winning” means something entirely different when removed from a game and applied to the real world. Real life is different from mathematics—the former is notoriously much less predictable and well-behaved than the latter. We don’t want one political party or another to win—we want a functioning government.

Taking the “the nuclear option” will obliterate the infrastructure of checks and balances within the Senate, the framework created to force our lawmakers to come to compromise. Thoughtful Republican Senators are right to be queasy about this. As the president’s poll numbers continue to drop, a move to simple majority in the Senate could come back to haunt them. Once again game theory rears its head: In the nuclear setting game theorists recognized the dangers of a “first strike” that was not a last strike. That realization became the heart of a strategy of mutually assured destruction that held the uneasy equilibrium of the Cold War.

So where does all this leave us? Axelrod’s postmortem of his tournament yielded four famous lessons for overall success over time, among which was “forgiveness.” This allowed for the restoring of cooperation but only in the face of an olive branch proffered by the opponent. It also suggests that even as a self-interested actor, Trump should be looking for partners. Nuclear gamesmanship suggests that a first strike is a mistake, since in time, a retaliatory strike may very well ruin the striker and possibly all of us in a political nuclear winter. If only a few more of our Senators—or at least one—had been a math major, perhaps we wouldn’t find ourselves on the brink.