fatvegan

My smug economic lecturers once told us very smugly that the problem with governments can be summarised by Kenneth Arrow's Impossibility Theorem. It's the idea that you can't ask everybody what they want and as a group do something that makes everybody happy. The gist of Arrow's paradox is that it's impossible to aggregate preferences.

I reckon it's a bit of a silly paradox, for two reasons. The first is that, for lots of stuff, we have to aggregate preferences. Even imperfect aggregation is unimaginably better than not aggregating. Airports might be one example. So saying we can't aggregate perfectly isn't very helpful, because we're going to do it regardless. The theorem is used as an argument against government intervention, but markets and governments are simply two different ways of doing a similar thing. Markets probably aggregate preferences more "neatly" because dollars are more divisible than votes, but that doesn't necessarily make the outcomes better. You could divide votes up more if you wanted, so they functioned more like money. The problem with that being that we'd become more democratic and we don't want that because the people can't be trusted to know what's right.

I quite like the way the market works things out. I like the way it gets a whole lot of smart minds working at solving problems and sharing in the benefits. And I actually do think that for the smart minds at least, they do share in the benefits. I reckon that if you have a way of redistributing wealth than it's hard to beat most market outcomes. But there are also plenty of ways where I suspect the market is worse than governments (even mediocre governments) in terms of both fairness and efficiency. Aggregation is a very tough thing to do, whoever is doing it. There are lots of areas where making all your best brains work together will get you a better outcome (probably a lot of research). And areas where I don't think your wealth should equal the number of votes you get (probably all health care and pre-tertiary education).

Update: My original point I forgot to make. If it's interesting to anyone at all, it probably only is to people who already know how the theorem decides it's impossible. And they've probably already thought of the same point themselves.

Ahem. Ahem. I have a theory. And it is that the voting system assumed by the Impossibility Theorem only collects a limited amount of information about people's preferences. It asks people to order a list of things and a thing's place on the list represents their vote. But you can definitely collect more information about someone's preferences than that. Although it will be more complicated and might involve fractions. Alternatively, sticking a bunch of people in a room and not letting them out until they can collectively tell you what they want you to spend this year's tax revenue on also works. Preference aggregation isn't about making everyone happy. At the best you hope that everyone will feel the outcome was reasonable.