[EM] Anyone got a good analysis on limitations of approval andrange voting?
Jobst Heitzig
heitzig-j at web.de
Tue Nov 17 01:51:33 PST 2009
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.
> ----
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