[EM] Theoretical Justification for "Winning-Votes"

[Markus Schulze]

Dear participants,

I have uploaded the paper "Monotonicity and Single-Seat
Election Rules" (Voting Matters, issue 6, page 9-14,
May 1996) by Douglas R. Woodall:
http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf

In this paper, Woodall introduces the so-called
"plurality criterion":

> Plurality: If some candidate x has strictly fewer votes
> in total than some other candidate y has first-preference
> votes, then x should not have greater probability than y
> of being elected.

Woodall writes:

> Election 3
> ab 11
> b 7
> c 12
>
> (...)
>
> It seems that most of the Condorcet-based properties
> discussed in the Social Choice literature would in fact
> elect a in Election 3, and so violate plurality (whereas
> AV elects c and DAC elects b). How seriously one regards
> the failure of plurality depends on how one interprets
> truncated preference listings, and that in turn may
> depend on the rubric on the ballot paper. If the 12 c
> voters are merely expressing indifference between a and b
> and not hostility to them, and so can be treated in
> exactly the same way as if half of them voted cab and half
> voted cba, then the violation is not too serious. But if,
> by plumping for c, these voters are not just saying that
> they prefer c to a, but that they want c and definitely
> do not want a (or b), and if the seven b voters also
> definitely do not want a (or c), then it is clear that c
> has more support than a and so a should not be elected.

The beat path method and the ranked pairs method satisfy
plurality only when the strength of a pairwise defeat is
measured by the absolute number of votes for the winner
of this pairwise defeat, but not when the strength of a
pairwise defeat is measured by its margin.

Markus Schulze