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

[Kristofer Munsterhjelm]

On 22.01.2022 20:53, Kevin Venzke wrote:
> 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.

I'd say that IFPP's improvement for three candidates (and moreso fpA-fpC
or Smith,IFPP) is that it has the kind of strategy resistance that's
only (out of methods commonly discussed here) shared by IRV and
Smith-IRV hybrids respectively; and it does so while being monotone. So
it's evidence that you can have a monotone method that's robust to
strategy, and since every three-candidate minimally strategic method
seems to lie pretty close to it, it would presumably be a good building
block for a fully general such method.

Craig, of course, was not trying to find a Condorcet method and IIRC he
considered the Condorcet criterion to be inexpressible in his framework
(although I think that if I had been around then and had known what I
know now, I could've explained it in terms he'd have understood). He was
trying to find something that could pass as much of LNH and mutual
majority as possible while still being monotone. Fortunately for us, "as
much LNH as possible" ended up giving DMTBR when combined with Condorcet.

I suspect that if you have a base method X that passes DMT and DMTBR,
then Smith,X also passes it. (It'd be nice to have proof of this, and
particularly also Landau,X.)

> 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.

I had the impression he had a number of not quite formed prototypes but
couldn't get where he desired with them.

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

Right. Perhaps I don't have an intuitive sense of just how restrictive
it is, and so I think it's possible where it's not :-)

But if it's not possible, then there should be a Moulin-style proof of
it. Perhaps there's a relation between the kind of differential
constraint observations I've been doing and such proofs. A good first
step/example of this would be to convert my proof ideas for showing
unmanipulable majority incompatible with Condorcet, into a Moulin-style
exhaustive proof. I'd have to develop my theory a lot more before I
could do that, though!

-km