[EM] DMTCBR and reversal symmetry

[Kevin Venzke]

Hi Kristofer,

Le lundi 24 octobre 2022 à 04:43:58 UTC−5, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit :
> Thus a method that passes both DMTCBR and rev. sym. would be extremely
> resistant to both burial and to compromise. But since the favorite
> betrayal criterion is so hard to pass, we have reason to believe that
> this is impossible. So no such method can be rev. sym -- which is what
> we at least see with Condorcet methods!
> 
> It's thus quite that the implication is stronger: that we can't have all
> of DMTBR, majority, and reversal symmetry. But the proof is probably a
> lot harder to find, too.
> 
> So all of the above implies that when creating a resistant ranked
> method, we can't both have extreme resistance to burial and compromising
> - we have to pick one. Fortunately (as James Green-Armytage originally
> showed), we already get a great deal of compromising resistance from the
> Condorcet criterion itself (since, for instance, it does the right thing
> under center squeeze). Thus it's more sensible to choose further burial
> resistance over further compromise resistance if we can only have one.
> 
> (Unless we consider maximum compromise resistance absolutely
> non-negotiable, e.g. Mike O's insistence on the FBC.)

Well, insisting on weak FBC would rule out Condorcet. Maybe a better example would
be my "Condorcet Compromise Extension":
votingmethods.net/cce

This proposes a (convoluted) way to make use of the fact that in all Condorcet
methods there are possible results under various scenarios that would necessarily
create compromise incentive. So we can simply directly try to avoid those.

As I've suggested before, I don't share the feeling that we should say that
Condorcet inherently ensures adequate compromise resistance, and from there try to
maximize burial resistance. I think the worst Condorcet methods wrt compromise
incentive are to be sure not worth advocating.

What I think instead is that voters will see burial under Condorcet as an
unattractive, excessively risky option provided that:
1. voters have a natural inclination to truncate the options they like less than
the best frontrunner (as opposed to ranking them sincerely, or using burial). And
2. truncation is an effective defensive strategy under the method.

#1 I believe is just true. #2 we can certainly foul up. (Without #2, offensive and
defensive strategy become indistinguishable: Burying the worse frontrunner may not
be an attempt to steal a win, but to thwart someone else trying to steal it.
Voters need to feel that truncation is a sufficient defense, so they don't do
this.)

I'm assuming generally that the way the burial strategy works is that A voters
falsely rank non-viable candidate C over rival frontrunner B, and expect that B
voters will prevent a disaster by reporting that A is better than C. But I wonder
in what scenarios that is realistic to expect? Some will say it's a shame if B
voters can't freely and safely vote B>A>C, as they really feel, but to me it is a
luxury, when A vs B is the only real question to be answered in the election.

Kevin
votingmethods.net