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

[Raph Frank]

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.