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

[Michael Ossipoff]

Oops! Thanks for pointing that out. It convincingly seemed to me that
dropping the weakest defeat in every cycle would do exactly the same as the
Ranked-Pairs procedure, where you make a list starting with the stronger
defeats, skipping any defeat that cycles with listed defeats.

Evidently not so.

The definition that I gave results, as you said, in a tie—even if all the
defeats are different magnitudes, & there are no pair-ties.

So that tie with B & C unbeaten would happen even in any big public
election.

Again, thanks for telling me about that. As you can tell, I was so sure
that I didn’t even try a multi-cycle example.

So much for my briefer RP definition-wording.

But RP still seems easier to define & explain than Beatpath/CSSD.

Also, Steve said that the RP winner usually pairbeats the Beatpath winner.

Is River as easy to define &. explain as RP?.

Fortunately,  all Condorcet(wv) methods are the same with 3 candidates. So,
in my 18 cases with only 3 candidates, my wrong definition didn’t make any
difference, with just that one cycle.

But in a larger election, the buriers might bury CW under 2 Buses, making 2
parallel cycles both involving CW & BF, but each cycle with a different Bus.

I hope that doesn’t affect RP’s autodeterence when the right definition is
used. I should try that with MinMax too.

BTW, I added 6 more cases, with the CW faction half ranking BF 2nd, & half
ranking Bus 2nd…summing to 4 ways for the CW voters to 2nd-rank:

CW>BF
CW>Bus
CW
Half each of CW>BF & CW>Bus.

It just seemed to more realistically cover how toCW voters could vote.

That brought it to 24 cases.

It raised the Bus/BF ratio from 7 up to 10.

There was a journal paper with the words “Split-Cycle” in its title. The
author defined Split-Cycle the same way as my incorrect brief RP
mis-definition. He said it was different from RP. Ain’t that the truth !

He used margins instead of wv, & claimed all sorts of fantastic
criterion-compliances for it…presumably in natural sincere circular ties.

I didn’t know what he was talking about.

Well, with luck, the autodeterence will still work , with the right RP
definition in multi-Bus examples.

Thanks again for pointing that out to me.



On Wed, Feb 28, 2024 at 22:41 Kevin Venzke <stepjak at yahoo.fr> wrote:

> 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)
>
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