First preference Copeland

First preference Copeland is a variant on the Copeland method. It was devised by Forest Simmons in 2006. The name is due to Kristofer Munsterhjelm.

In first preference Copeland, each candidate is assigned a penalty: the sum of first preferences of the candidates that beat the candidate pairwise. The candidate with the least penalty wins.

First preference Copeland passes Smith because supposing otherwise, that some candidate Y not in the Smith set wins; then for a candidate X in the Smith set, Y is beaten by every candidate X is beaten by, and some more. Thus Y's penalty must be higher than X's, so Y couldn't have been the winner.

However, FPC fails both independence of clone alternatives and the monotonicity criterion. One example of monotonicity failure is as follows:

8: A>B>C
2: A>C>B
9: B>C>A
12: C>A>B

and C wins. Then raise C on the two A>C>B ballots:

8: A>B>C
9: B>C>A
14: C>A>B

and A wins.

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