[EM] Ordering defeats in Minimax

[Kristofer Munsterhjelm]

On 04/25/2017 03:34 PM, Kevin Venzke wrote:
> Yes, WV satisfies Plurality. In fact margins methods are among the only
> serious proposals that don't satisfy it. This property
> says that e.g. A can't win in this scenario:
> 
> 7 A>B
> 5 B
> 8 C
> 
> Methods that have added Smith compliance to MinMax usually call for
> WV. Schulze's paper describing the Schulze method
> used to say that there had been discussion concluding that margins
> wasn't recommended due to strategic reasons, though I
> can't find that language there anymore. That being said, I would be a
> bit surprised to learn that anyone using Schulze has 
> chosen a margins version of it.

>From a criterion perspective, that makes sense. Smith,Minmax doesn't
pass mono-add-top anyway, so you might as well pick up Plurality on your
way by going wv.

> The issue is pretty controversial and becomes complicated when you get
> into the strategic implications. Arguments that 
> margins just "makes more sense" than WV are common, but I find them
> rather abstract in comparison to what I think voters
> would expect from a method.

Warren wrote about wv versus margins here:
http://rangevoting.org/WinningVotes.html and seems to have reached
roughly the same conclusion. That is, that margins can in some ways be
more "natural", but wv is more strategy resistant. (He then says that it
doesn't much matter because both wv and margins are vulnerable to DH3. A
method like Smith,IRV is more robust to DH3, but wv vs margins doesn't
matter to that method.)

> As an example of the latter, suppose there is only one pairwise contest
> A>B in which all of the voters expressed a strict
> preference. Say it was very close, 51%-49%. The margins logic is that
> this contest is fair game to be discarded because of
> how close a race it was. But I would say that this contest is probably
> the one that the voters view as the most important one,
> everyone having voted on it, and they would not expect its loser to be
> elected. They (at least the 51%) will likely view this
> as a spoiler situation, as whatever other candidates were in the race
> (to cause this outcome) did not themselves win; they
> simply threw the race to the candidate who (without their presence)
> would have lost.
> 
> The desire to say that a 35-0 win is stronger than a 51-49 win could
> make sense if a strong win in itself was of some value.
> But all that realistically matters is who wins the entire race. If the
> 35-0 winner is not in a position to get elected, there is 
> nothing to be gained in letting that contest affect the outcome. It
> doesn't aid him or his supporters, it is pure noise. It could
> as well be treated as zero strength.
> 
> Kevin