Dear folks, there is another assumption in Arrow's theorem which people almost always forget: Determinism. Methods which use some amount of chance can easily meet all his other criteria, the most trivial example of this being again Random Ballot (i.e. pick a ballot uniformly at random and copy its ranking as the group's ranking). Some people think this violates the no-dictator requirement, but it doesn't since a dictator would be a person determined *beforehand*.
Yours, Jobst Raph Frank schrieb: > The theorem states (from wiki) that there is no method which has the > following properties: > > * If every voter prefers X over Y, then the group prefers X over Y. > * If every voter prefers X over Y, then adding Z to the slate > won't change the group's preference of X over Y. > * There is no dictator. > > All 3 of those conditions are met for range. The only problem is that > adding Z could cause renormalisation changes in how people vote. > > A voter who votes > > A: 100 > B: 0 > > might change vote to: > > A: 100 > B: 50 > Z: 0 > > after Z is added. > > Thus changing the difference between A and B for that ballot. > > Ranked systems allow full ranking. Adding another candidate just > requires that you insert the candidate into the rank order. > > With range this might not be possible. If the candidate has a rating > outside the max and min, a voter may have to rescale their prior > preferences. > > If the assumption is that voters are just allowed add a rating for Z > and not change any of their other ratings, then it meets the 3 > conditions and thus is a counter example to Arrow's theorem. > ---- > Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
