Here's an heuristic argument showing why proxy approval is apt to pick the
CW when there is one, regardless of the dimension of the issue space.
When there is a CW, rational approval players with perfect information
will concede the win to the CW, because the CW is the one and only stable
equilibr
My previous argument can be extended to the case of N candidates, 1 seat,
and 1 dimensional issue space:
Let the letter X represent the candidate that the voter median is nearest
to on the (one dimensional) issue spectrum.
This "Voter Median Candidate," X, is the Condorcet Winner.
To show that
Candidate Proxy with 3 candidates, 1 seat to be filled, and a 1
dimensional issue space:
The following conditions taken together are sufficient to ensure that the
Candidate Proxy Winner and the Condorcet Winner will be one and the same
in a three candidate, single winner election.
(1) The issue s
