[EM] Quick and Clean Burial Resistant Smith, compromise

[Kevin Venzke]

Hi Kristofer,

Le samedi 8 janvier 2022, 17:21:22 UTC−6, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit :
> > I have a hunch that if you put your "strategy-resistant Condorcet" hat on and
> > evaluate C//FPP, you will find it to be "good."
> 
> In my Monte Carlo (non-exhaustive) simulations, there are generally
> three types of methods as far as strategy resistance goes: the type
> that's susceptible >90% of the time whatever the number of candidates,
> the type that's ~30% but increases with number of candidates to very
> high levels with lots of candidates, and the type that's low and doesn't
> increase.
> 
> A method is susceptible to strategy in a particular election if the
> honest winner is A but voters who prefer some other B to A can conspire
> to get B elected by changing their ballots.
> 
> C//FPP is the first type. MAM, Schulze, minmax, etc are of the second
> type, and Smith-IRV, Benham, and fpA-fpC are of the third type.
> 
> Each election is a one-shot game (first some candidate wins, then
> factions get to try to make other candidates win); there's no defensive
> strategy. So it probably resembles your "never looks attractive in the
> first place" setting.

Interesting. I suppose the obvious burial scenario for C//FPP is just every
single scenario where there's a CW who is not the FPW.

>From scenarios I've been able to generate, it seems to me that fpA-fpC is purely
a middle ground between C//FPP and C//IRV. (Looking at three candidates.) I have
not, I think, seen a scenario where fpA-fpC, in a cycle, elects the FP loser, or
elects a non-FPW who didn't beat the FPW pairwise.

In other words, fpA-fpC usually likes the C//FPP winner, but sometimes it
prefers the second-place first preference candidate, provided they beat the
first preference winner. (Incidentally, my proposed expansion to fpA-fpC doesn't
maintain this pattern...)

It surprises me that you measure C//FPP to be in a whole other category, of
high manipulability, when in "method space" it is so close to those third type
methods.

I wonder how you categorize BPW and SV? I find them to be quite distant in
method space from those third type methods. But by my strategy measures they
seem attractive, with less compromise and burial incentive. The truncation
performance is comparable/mixed. It's just mono-raise and mono-add-top where BPW
and SV look unusually bad.

If you would want a 4+ candidate version of BPW (for example in order to
determine whether it is "second type"), you can use "first preference chain
climbing." Start with an empty set. Go down the list of candidates sorted by
first preference count, descending. When a candidate beats all candidates (if
any) in the set, add them to the set. Elect the last candidate you can add.

Kevin