[EM] Quick and Clean Burial Resistant Smith, compromise

[Kristofer Munsterhjelm]

On 09.01.2022 00:58, Daniel Carrera wrote:
> 
> 
> On Sat, Jan 8, 2022 at 5:21 PM Kristofer Munsterhjelm
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
> 
>     On 08.01.2022 23:37, Kevin Venzke wrote:
> 
>     > 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.
> 
> 
> Wow. What type is Ranked Pairs? Is Ranked Pairs is part of the "etc"?

Ranked Pairs is in the minmax group (second type).

> Is there an intuitive explanation why Smith-IRV and Benham are more
> resistant to strategy? I'm trying to find Behman's method on the 
> electowiki but I'm not finding it. I was sure I had seen it there 
> before. Does it have an alternate name?

Perhaps you misspelled it - it isn't Behman but Benham. You should be
able to find it at https://electowiki.org/wiki/Benham's_method :-)

As for why the Condorcet-IRV methods resist strategy better, I think
it's a combination of dominant mutual third burial resistance (which
also renders the method immune to the DH3 scenario) and chicken dilemma
resistance.

An example of the three categories can be seen on the left in
https://www.votingmatters.org.uk/ISSUE29/I29P1.pdf, on page 8. Borda is
in the top category, minmax is well, in minmax, and IRV and the
Condorcet-IRV hybrid (Woodall) are at the bottom.

Unfortunately, pretty much every method in the resistant category is
nonmonotone. fpA-fpC (which Kevin calls my Linear method) is monotone
and passes both DMTBR and chicken resistance, but I don't know how to
extend it to a Smith set of more than three candidates.

It should be possible - my integer programs have found optimally
resistant methods for more than three candidates, for a low number of
voters, but only in lookup table form. The results show that insisting
on monotonicity doesn't make the methods any more susceptible to
strategy, at least not with few voters. But how to do it remains a
mystery, still.

-km