A Mathematician reads the New Yorker, or, Math for votesJuly 27, 2010
This week’s New Yorker features an article on voting, and it’s a good read. What does this have to do with mathematics? Well, mathematicians have been thinking about building the best kind of democracy for some time, and the unpleasant result is, it seems to be impossible to have a voting system that represents the people’s will perfectly. The actual mathematical result, known, delightfully, as Arrow’s Impossibility Theorem, isn’t quite that cut and dry, but let’s just say if you think a perfect democracy that executes the will of the people with absolutely minimal distortion is a naive fantasy, you can find some things in math to back you up.
Not that we shouldn’t aspire to improve our voting system. There just seems to be some difficulty to it.
A suggestion I’ve only heard once, and that I love, for all it’s counter intuitiveness, is a randomized democracy. That is, people are appointed to office by random selection, as in jury duty, possibly with some major kinks to work out. Making sure that they’re sane, for example.
Why would randomness be a good thing? It’s a tough sell, but consider it. No campaign contributions, no ambition, no selling out for your next campaign. We’d have to get serious about educating everyone because our next leaders could come from literally anywhere. And, the introduction of randomness makes it much harder to game the system, or for the system to become calcified. You generally end up with something more robust.
I don’t know what a feasible version of a random democracy would look like, but one thought might be a chaotic enough one that simulated a kind of randomness. Often by applying a process over and over again in the right kind of strange way, you can get something that’s close enough to random for all practical purposes. Think of a feedback loop when you take video of a TV screen that’s displaying the video: it’s almost totally random. What would this look like in democratic decision making? Consider this passage describing the middle ages process of picking a new doge:
Not conducive to the spirit of democratic openness or simplicity, I grant you. But kind of random, you might think, in the same way that feedback is, and it’s there for the same reason nature introduces randomness: it makes systems robust.