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Some background on the problem this is trying to solve: There are a handful of mathematical theorems that basically say "there is no perfect voting system." Mo

by lmkg 16y ago

Some background on the problem this is trying to solve: There are a handful of mathematical theorems that basically say "there is no perfect voting system." More rigorously, they enumerate a list of desirable properties that you would like voting systems to have, and show that NO voting system can have all of these properties, because they are actually contradictory. Some of these properties are things that are "obvious" ones that any practical voting system should satisfy: voting matters, there is no dictator, candidates can win, determinism. Two of them are non-trivial: absence of tactical voting, and irrelevance of independent alternatives (IIA). Tactical voting basically means you have a game-theoretic incentive to vote in a way that differs from your true desires. IIA basically means that if Gore would win a 2-man election against Bush, adding Nader to the race should not make Bush the winner. These properties are related, but not the same. All of these properties are desirable, and a "perfect" voting system would have all of them, but you can't have all of them. You have to pick at least one to give up. Tactical voting in particular is extremely hard to remove, even if you give up IIA, while systems that satisfy IIA are somewhat complicated. The article suggests that it is very easy to satisfy all of the other criteria, if we let go of one of the "obvious" criteria: determinism. So it's basically a question of picking your poison. You can have determinism, or you can get rid of tactical voting, but you can't do both. The author is contending that determinism is the best property to give up. Further reading: http://en.wikipedia.org/wiki/Arrows_theorem http://en.wikipedia.org/wiki/Arrows_theorem is one of the mentioned theorems, dealing with ranked-preference voting systems (vote-for-one-candidate is a special case). There are a few others for different classes of voting systems.

DRMacIver 16y ago
As a side note, this does not directly address the problem proposed by Arrow's theorem, although it could easily be made to do so, but the post isn't so interesting in that context. It's more about how it interacts with a constituency system. If you want a randomised solution to Arrow style preferential voting, the following is the best I currently know of: 1. If you have one candidate, stop. That candidate is elected. 2. If you have more than one candidate, pick a candidate at random. Call that candidate Pivot. Every candidate who the majority thinks is worse than Pivot drops out of the race. If there is no one the majority thinks are worse than Pivot, Pivot drops out. 3. Goto 1. Edit: Err. Correction. That's an algorithm for selecting a single winner from Arrow style preferential voting. It's based on an only slightly more complicated one for giving you the full range though.
logicchop 16y ago
The condition you identify as "IIA" isn't Arrow's condition. IIA in Arrow's theorem is best understood as the principle that only information on the ballot is relevant to the vote. The condition you cite is a much stronger counterfactual property: that if x beats y, then x beats y even if we introduce z. But this is not Arrow's condition (see Bordes and Tideman on this).

by lmkg 16y ago

DRMacIver 16y ago

As a side note, this does not directly address the problem proposed by Arrow's theorem, although it could easily be made to do so, but the post isn't so interesting in that context. It's more about how it interacts with a constituency system. If you want a randomised solution to Arrow style preferential voting, the following is the best I currently know of: 1. If you have one candidate, stop. That candidate is elected. 2. If you have more than one candidate, pick a candidate at random. Call that candidate Pivot. Every candidate who the majority thinks is worse than Pivot drops out of the race. If there is no one the majority thinks are worse than Pivot, Pivot drops out. 3. Goto 1. Edit: Err. Correction. That's an algorithm for selecting a single winner from Arrow style preferential voting. It's based on an only slightly more complicated one for giving you the full range though.

logicchop 16y ago

The condition you identify as "IIA" isn't Arrow's condition. IIA in Arrow's theorem is best understood as the principle that only information on the ballot is relevant to the vote. The condition you cite is a much stronger counterfactual property: that if x beats y, then x beats y even if we introduce z. But this is not Arrow's condition (see Bordes and Tideman on this).