# [EM] A Metric for Issue/Candidate Space

Forest Simmons fsimmons at pcc.edu
Mon Dec 7 21:56:11 PST 2020

```How to define such a metric?

How to use it?

Ask the voters which issue they felt to be most important, and which pair
of candidates were the farthest apart on that issue. The pair with the most
votes is taken to be at unit distance ... the others at distances
proportional to their respective mentions.

Use it to in conjunction with the pairwise margins matrix as follows: for
each candidste X, let S(X) be the set of candidates that beat or tie X
pairwise. In particular X is itself a member of S(X) by virtue of a self
tie.

Elect the candidate X that minimizes the diameter of S(X).

Note that if S(X) has only one member then that member is the Condorcet
Winner, and the diameter of S(X) is zero, the absolute minimum.

So the method is Condorcet Compliant.

It seems pretty obvious that it satisfies clone independence.... and mono
raise.

Anybody else like this?

How about using it for tournaments? What questions would you ask the fans
to estimate the distances between teams?
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