[EM] Strategy-proof vs Monotone, IFPP, Mono-add-top

[Kevin Venzke]

Hi Kristofer,

Le mercredi 19 janvier 2022, 08:57:59 UTC−6, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit : 
> However, monotone strategy resistant Condorcet methods are very hard to
> understand. I'm still trying to devise a method that's Condorcet, DMTBR,
> and monotone, but I haven't had much luck yet. I know through (more or
> less) exhaustive search that for three candidates, fpA-fpC and
> Smith,Carey are close to optimal. But as Craig himself pointed out,
> generalizing to more than three candidates is very tough.

I was thinking, with Carey it seems like we should be able to say conclusively
that it can't be expanded to 4+ candidates. What stumps me though is that I'm
not sure how to explain what IFPP's improvement over FPP is supposed to be.
I guess we would have to say it's "more" clone independence, to get as much of
it as you can without sacrificing LNHarm, LNHelp, and Mono-raise. Then perhaps
it might be that 4+ IFPP is actually just FPP.

But I seem to recall that Craig did have an imperfect 4-candidate method
(whose definition was possibly not really expressible) that sacrificed
properties differently than that.

> Of course, the same can be said about Smith and mono-add-top. I suspect
> that in the case of complete ballots, Smith is not incompatible with
> mono-add-top, although the question remains open (and is seemingly very
> hard to prove or disprove).

I think it's hard only because we need to see what the actual scenarios and
ballots are which will run you into a contradiction. If you take Mono-add-top
and translate it to its "worst case" demands purely in terms of the graph of
wins/ties/losses, a daunting picture forms.

In the worst case, MATop's operation means leaving all of the winner's pairwise
contests unchanged (directionally), while *every* other contest is free to
change. In a Smith+MATop method, the MATop operation can't be allowed to remove
the winner from the Smith set. This means that the winner of such a method must
always be in the Smith set without reliance on any contests besides his own.

I think it's safe to say that the Smith set doesn't always have such a
candidate. In that case, this modified version of MATop isn't compatible with
Smith.

So, if Smith and MATop are compatible, it must be that for some reason, MATop is
not actually as demanding as it seems to be. That is, if the winner's Smith
membership depends on two other candidates' contest, for some reason in all such
cases under that method, we are assured that the MATop operation will not
disrupt that contest. Or else, that MATop will necessarily give that winner
additional pairwise wins that manage to keep him in the Smith set.

To me, it's too much to hope, that there is some technicality that will let us
do this.

> However, Smith and the plurality criterion
> combined are incompatible with mono-add-top. If asked, I would say that
> the former is better than the latter, but I couldn't justify this
> particular decision. There's ultimately some aspect of value judgement
> to all of this.

I suppose, but practical arguments occur to me, even if some of them are based
on what I think *other* people's value judgments are.

Being a subset of Participation, Mono-add-top failures create complaints for a
specific selection of voters. It may be hard to nail down who exactly may or may
not be in that selection. That reduces the power of the complaint, I think.

I try also to imagine the complaint of a *candidate* who believes they have been
wronged by a MATop failure. He argues that if you delete a specific selection of
his votes, along with all other info on them, then he would have won. That feels
a bit weak to me as well.

Kevin