[EM] The Schulze & RP(wv) determined to be very strongly probabilistically autodeterrent.

[Kevin Venzke]

Hi Mike,

Interesting work:

Feb 24 2024 à 16:39:27 UTC−6, Michael Ossipoff <email9648742 at gmail.com> a écrit :
> Schulze, RP(wv), MinMax(wv) & Smith//MinMax(wv) are all very strongly
> probabilistically-autodeterent.
> 
> I applied them to a typical example with a complete exhaustive set of 18 cases.
[...]
> When I introduced Condorcet(wv), & told its properties, 35 years ago, they
> included compliance with what is now called the Minimal-Defense Criterion.
> 
> Because of the possibility of defensive truncation being used, that
> criterion-compliance conferred burial-deterrence.
[...]
> Those methods are the only ones that have been determined to be
> probabilistically autodeterrent by exhaustive testing.
> 
> Given that Schulze & RP are widely popular & widely recognized as the kings of
> criteria-compliance, & given the extreme brevity possible for RP, RP(wv) is the
> obvious natural best proposal for a Condorcet-Criterion rang-method.
> 
> RP(wv):
> If no voted CW (due to a top-cycle):
> Drop the weakest defeat in every cycle.
> Elect the resulting unbeaten candidate.
> (Defeat-strength measured by number of ballots ranking defeater over defeated.)

Putting aside popularity or name recognition I tend to think that River
dominates RP due to ease of calculation, whether one performs it manually or
has to write an algorithm. I guess maybe you didn't check River, but I think
it would evaluate the same.

I like your conception of RP here, which looks pretty easy, but I wonder if it
leads to ties.

For example, if there is a cycle A>B>C>A where B>C is the weakest among these,
and also a cycle A>B>D>A where A>B is the weakest, do we drop B>C and A>B
simultaneously? If we do, it starts to look like we won't know how to order B
relative to C in the final ranking.

Kevin
votingmethods.net
votingmethods.net/cond (relevant Condorcet calculator)