[EM] Anyone got a good analysis on limitations of approval andrange voting?

[Jobst Heitzig]

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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