Arrow's impossibility theorem

But Arrow's theorem is first and foremost an exercise in logic. It is grossly oversimplified, and therefore should not be treated as realistic simulation of real-world voting systems. We should be very careful when drawing political conclusions from logical proofs.

There are several reasons why most contemporary political theorists don't give a damn about Arrow's theorem, despite its logical plausibility.

1) Arrow's theorem assumes everyone's preferences to be fixed points, and only cares about finding a curve that fits all of those points. But people's preferences are not fixed. People are always changing their minds, often in response to the shifting preferences of others. Many political theorists in the "deliberative democracy" camp (the dominant model since the early 90s) argue that the whole point of a democratic discussion is to get people to reconsider their pre-existing preferences and find some sort of middle ground.

2) It's not even clear why an ideal procedure would need to satisfy all of the preferences, or even most of them. If making everybody happy were as simple as designing an election procedure, we would have gotten rid of politics a long time ago! You don't even need 3 or more preferences to arrive at a conflict. Two people with one preference each, that directly contradict each other, would be enough to produce a situation where no procedure can satisfy them all. In other words, there's nothing new here. Time to move on.

3) Arrow's theorem is somewhat effective in explaining how the actual share of seats in a lawmaking body can end up being very different from the number of votes that each party received in a first-past-the-post voting system with 3 or more major parties, such as UK and Canada. But there are much simpler, more intuitive ways to explain that.

All in all, Arrow's theorem was a neat response to the political theory of the mid-20th century, when people assumed democracy to be simply a matter of efficient curve-fitting. But political theory has come a long way since then, partly in response to problems like Arrow's theorem. In the new academic milieu, Arrow's theorem isn't as relevant as it used to be.

On the other hand, I can sort of imagine how Arrow's theorem might find a new use in designing distributed computer systems. Since computers aren't as fickle as human politicians, the logical conclusions of Arrow's theorem might be more relevant there. It's good to see that the HN thread so far focuses more on technical details than on grand, mostly irrelevant political narratives.

Say there's an election between a moderate democrat "blueberry pie" and a third party liberal "apple pie". As a liberal, Sidney would rather vote for the third party ("Sidney orders the apple pie"). However, if you introduce a republican candidate "cherry pie", Sidney will probably vote for the democrat (blueberry pie) instead of the third party candidate, because he'd be worried about his vote costing the more moderate candidate the election.

IIA means that you won't vote differently than your preferences—but people do that all the time. And sure, a voting system where that wasn't necessary would be nice, but losing that condition isn't as nonsensical as it seems at first.

You're right that it was a smaller group, of course, but it wasn't an empty one.

Jello Biafra's endorsement of Nader plus Gore's attack on Twisted Sister for the Parents Music Resource Council means N-B-G was actually the order of preference for anyone where "the right to rock out" was their single voting issue.

(I was young, ok?)