Copeland's method: Difference between revisions
Clarify the Smith proof so that it holds for Copeland's victories-defeats formulation as well.
Psephomancy (talk | contribs) (start using ballots template, we can always change the stylesheet) |
(Clarify the Smith proof so that it holds for Copeland's victories-defeats formulation as well.) |
||
Line 33:
==Criteria==
Copeland's method passes the [[Smith criterion]] because any candidate in the Smith set by definition beats everybody outside of the Smith set, but no candidate outside of it does so. For any candidate X in the Smith set and Y outside of it, Y is defeated by at least as many candidates as X, and X defeats at least one candidate that Y doesn't. Thus, every candidate in the Smith set must have a greater Copeland score than any candidate outside of it. Furthermore, the Copeland ranking of candidates (the ordering of candidates based on Copeland score) is a [[Smith set ranking]], since
(Example showing Smith members having only 2 points more than non-Smith members: Suppose there are two candidates, one of whom is the Condorcet winner, and thus the only candidate in the Smith set. The CW has one victory and no defeats for a Copeland score of 1, while the other candidate has no victories and one defeat for a score of -1.)
| |||