[EM] Quick and Clean Burial Resistant Smith, compromise

[Kristofer Munsterhjelm]

On 17.01.2022 21:11, Kevin Venzke wrote:
> 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.

It makes sense to me. I've later found out that fpA-fpC is very close to
Condorcet,Carey (as defined only for three candidates). And Carey is a
sort of compromise between IRV and Plurality; it's more like Plurality
so that monotonicity is satisfied, but not so much that it loses (single
candidate) DMTBR.

Suppose A is the Condorcet winner and has more than 1/3 of the first
preference votes. Then A is not eliminated in Carey: either both the
other two candidates are eliminated and A wins outright, or one
candidate is eliminated (say C without loss of generality) and then A
beats B pairwise due being the CW.

However, Plurality may choose another winner if the Plurality winner is B.

> 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.
I would imagine they would be in the third category. I haven't checked
in detail because, since they're all nonmonotone, they don't seem to
provide a benefit over just using Smith,IRV. Perhaps unlike Smith,IRV
they could be made summable, but that would depend on the continuation.

I suspect that continuations would have to do something in the vicinity
of solid coalitions to retain DMTBR. Being disproved by chain climbing
retaining the base methods' strategic resistance would be great, of
course :-)

-km