[EM] "margins vs. winning votes" and Woodall's "Plurality" criterion

[Markus Schulze]

Hallo,

Woodall's papers can be found here:

http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM
http://www.mcdougall.org.uk/VM/ISSUE6/P4.HTM

Woodall writes in his 1994 paper:

> 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.
>
> (...)
>
> 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.

In my recent mails, I wrote that Mike Ossipoff's concept
of "majority rejected" candidates cannot be used for other
election methods than MinMax. I also consider his concept
of "offensive" and "defensive" strategies not promising.

On the other side, Woodall's plurality criterion is a
criterion that can also be applied to other election methods
than MinMax. For example, also Schulze(winning votes)
and Tideman(winning votes) satisfy Woodall's plurality
criterion.

Markus Schulze