Glad I Didn't Stay Up
Seen off Rt. 117 in Chappaqua, New York

What We're Looking at Here Is a Nash Equilibrium

From Kevin Drum in the wee hours comes this insightful post:

A COUNTRY IN AMBER....Based on how the final few states are looking at the moment, the most remarkable thing about this presidential election is how nearly identical it is to 2000. Right now, it looks like no more than two or three states will flip from red to blue or vice versa.

As I said the other day, a difference of one or two percentage points makes a big objective difference, since one guy wins and the other doesn't, but it means almost nothing about the direction of the country. We're almost exactly where we were four years ago.

Which, really, is an amazing thing. You'd think an event like 9/11 would act as a catalyst that blows apart existing political dynamics and realigns the electorate, but instead it seems to have cemented it into place. Not only are we at the same place we were four years ago, but the divisions are actually more entrenched than ever.

It hardly seems possible that this can last forever, but if 9/11 didn't realign the electorate, what will?

And indeed, I can name four or five things that seem as if they've changed everything, but perhaps they've changed nothing. Perhaps US politics is locked into a Nash Equlilbrium, a concept in game theory originated by John Nash. Wikipedia has a good description of the Nash Equilibrium. Here is the most crucial bit:

A Nash equilibrium for a mixed strategy game is stable if a small change (specifically a infinitesimal change) in probabilities for one player leads to a situation where two conditions hold:
1. the player who did not change has no better strategy in the new circumstance

2. the player who did change is now playing with a strictly worse strategy
If these cases are both met, then a player with the small change in their mixed-strategy will return immediately to the Nash equilibrium. The equilibrium is said to be stable. If condition one does not hold then the equilibrium is unstable. If only condition one holds then there are likely to be an infinite number of optimal strategies for the player who changed. John Nash showed that the latter situation could not arise in a range of well-defined games.

Regardless of how Ohio comes out, neither political party got what they wanted from this election. That much is obvious.

(And it isn't pretty to have the election decided by a state where the wait to vote could be up to eight hours. Presumably, local government knows how many registered voters live in each precinct. There is no good excuse for this I can think of. Is Ohio some kind of fledgling democracy? Surely they've held elections before and have the know-how to apportion voting machines. Yes? For places that had really long waits someone must have set a maximum figure for acceptable voter turnout that is significantly below 100%.)

One somewhat creepy aspect of this election was the extent to which the candidates were similar. The New York Time remarks:

Since World War II, no two candidates have had such strikingly similar backgrounds of class and privilege, with so many points of overlap. These two not only attended Yale University two years apart, but were also members of the same secret society there, Skull and Bones.

There is a certain uncanniness to a political evolutionary process that would produce such similar candidates. This was not a Coke vs. Pepsi election in which the candidates were marketed as being as similar as possible like Bush vs. Gore. But in the fundamental things that we think or as molding human character, they are more similar than Bush and Gore.

Regardless of how Ohio turns out, it seems to me the biggest question is how we're going to get out of this box. If in fact we are looking at a Nash equilibrium, the only way out is to think outside the box; WAY outside the box.

UPDATE: I see that Jordan Ellenberg (Princeton mathematician and novelist) was exploring this idea on a more limitied scale in Slate on October 25th.

A FURTHER THOUGHT: A couple of people who know something about math have suggested that I'm oversimplifying. Well, of course I'm oversimplifying. The presidential election is way too complicated a system to make detailed mathematical arguments regarding Nash equilibria. But like the concept of fractals, where the existence of the concept gives you a feeling of recognition when you look at (say) a piece of cauliflower, I find the Nash equilibrium concept very suggestive of the current shape of US electoral politics.