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Wiki:ArrowsTheorem
Arrow's paradox
It is important to accept that all voting systems are necessarily broken, because of the Wiki:ArrowsTheorem. Real-world voting systems are more broken than most, but no voting scheme is perfect.
- I agree. But I find it quite ridiculous that you do not seem to see a space between "broken" and "perfect". This position is the crucial flaw of the VotingIsEvil argument. Voting is not supposed to be perfect, it's supposed to be optimal. The attempt to reach all decisions by consensus is naive because of the exponential likelihood of conflict as the group grows. This strategy is therefore utterly broken for large groups.
- Actually, you used the exact right word. All voting schemes are necessarily suboptimal.
- Broken is a value judgement and the theorem does not make such a judgement. Suboptimal is not precise, either, without specifying what the optimality criterion is. For all voting schemes to be suboptimal, they must be being compared to some other, optimal alternative (or an infinite chain of ever-better alternatives :) ). I don't think this is the case here. I think all you can say without actually stating the theorem is that "all voting systems have some undesirable characteristics" which doesn't really mean much.
- This isn't necessarily an argument against voting, though. ArrowsTheorem applies to all systems of choosing a single group action based on a number of conflicting individual preferences.
- Now, certainly, you can say it's better to come to a consensus, that is, to get individuals to change their preferences until they are all the same. However, if the alternative to voting is some other social method by which a single group action is chosen that not everyone agrees with, then ArrowsTheorem applies to that method, too. For example, imagine that after a discussion, some group members disagree with something that everyone else agrees with, but they decide to let it go; this method of ConflictResolution is subject to ArrowsTheorem.
Consensus decision making "fails" Arrow's theorem on at least two criteria:
- Universality. Sometimes, consensus decision making will fail to make a decision. This is by design: it is better to not come to a decision, than to come to a bad decision.
- Independence of "irrelevant" alternatives. The proposing of new alternatives is a key feature of consensus decision making, and those new alternatives can help reach consensus, even if the new alternatives are not selected in the end. This is by design: the alternatives are not irrelevant.
- Maybe monotonicity. Intuitively I expect it to fail monotonicity, but this is impossible to prove.
Arrow's theorem doesn't even prove that all voting systems have some undesirable characteristics - universality is sometimes undesirable. The independance of "irrelevant" alternatives is misnamed, as the alternatives are not irrelevant. Even "Citizen Sovereignty" is dubious: I want a conflict resolution system where the ranking of committing genocide against people outside the group can never be achieved from any set of individual preference ballots.
Voting is evil
ArrowsTheorem shows that no voting system--no matter how clever--can ever succeed in the face of strategic voting. The strategic voting doesn't need to be conciously held.
- All Arrow's Theorem does is define criteria that no voting system can meet. Big deal. Decision making is a tradeoff among timeliness, accuracy and participation. Simple majority rule is timely, nominally participatory, not very accurate. Others systems occupy different locations in the tradeoff space. Now, really, isn't this a more useful way of looking at voting than "no voting system can ever succeed"?
- Well, if you think that the criteria that Arrow's theorem gives are important, then I think it's important that we realize that these criteria cannot be met. It is good to know what it not possible so as to not waste time trying to acheive the impossible.
- However, as I pointed out on Wiki:ArrowsTheorem, I believe that a voting system can be "good" even if it doesn't meet the Arrow criteria. Specifically, I think it is okay to violate the Arrow criteria when a vote is "close"; a close vote to me means the "will of the people" are almost indifferent between the given options, so not much would be lost even if the result was chosen randomly in that case (except the illogical but sometimes necessary appearance of absolute legitimacy). -- BayleShanks
See VotingIsGood, VotingIsEvil