[EM] Hay guys, look at this...

[Kevin Venzke]

Hi Forest,

Le samedi 18 février 2023 à 13:19:10 UTC−6, Forest Simmons <forest.simmons21 at gmail.com> a écrit :
> Here's a simple, acceptable method that beats many elaborate Condorcet proposals including
> Copeland,Baldwin, Black, Nanson, MinMax, and many others. If it turned out that twenty
> percent of Condorcrt election had cycles in a certain odd ball electorate, it would still
> be a credible, upstanding choice.
> 
> It has a natural segue from the simplest definition of a Condorcet Winner into what to do
> if there is no CW:
> 
> A Condorcet Winner C is a candidate that is unbeaten pairwise. This means that for any
> other candidate X, the number of ballots on which C outranks X is greater than the number
> of ballots on which X outranks C.
> 
> In other words, C has a positive margin of support compared to any other candidate X.
> 
> If there is no candidate with a positive margin of support compared to every other
> candidate, then elect the candidate with the single greatest margin of support relative to
> any other candidate.

I'll call this method C//MaxMargin or C//MM.

One reason I can "live and let live" in regards to C,FPP is that it at least satisfies the
Plurality criterion. I think methods that fail this will be hard to propose.

(I also think that being likely able to guess which candidate will benefit from a burial
strategy in C,FPP might at least create some stability there, even if the ultimate result
might be compromise incentive / nomination disincentive, whenever voters perceive that
supporters of the FPP winner have a burial strategy that can't be defended against in any
other way. Put differently, I don't think we would see backfiring burial strategies under
C,FPP, due to the one-sidedness of which voters would want to try burying.)

Realistically C//MM resolves cycle scenarios by electing the candidate with the biggest win
over the weakest candidate. (The winning score probably won't come from a match-up between
strong candidates.) This gives it a good share of the truncation incentive seen under
C//Approval, as it's very clear that adding a lower preference for some candidate could
hand them the win.

But (experimentally) C//MM doesn't see C//A's reduction in burial incentive, perhaps
because you are using the margin, so burial can be used to undermine a candidate even if
you don't defeat that candidate. This is also easy to imagine: A few random voters casting
insincere votes burying a frontrunner could certainly be enough to take the win away from
them.

When it comes to compromise incentive, C//MM is considerably better than C,FPP, although
hardly amazing. Compromise incentive is most relevant to the concerns about the use of FPP
in the method, so perhaps C//MM accomplishes its mission.

Kevin
votingmethods.net