[EM] Quick and Clean Burial Resistant Smith, compromise

[Forest Simmons]

Kevin,

Great data!

See my inline response to your astute musings below ...

El sáb., 8 de ene. de 2022 2:48 p. m., Kevin Venzke <stepjak at yahoo.fr>
escribió:

> Hi Forest,
>
> Le vendredi 7 janvier 2022, 18:28:06 UTC−6, Forest Simmons <
> forest.simmons21 at gmail.com> a écrit :
> > [Robert] opined ...
> >
> > "Probably Schulze or RP is the best thing to do for those cases when
> there is
> > no Condorcet winner.  But getting that into legislative language is
> difficult,
> > which is why I have advocated for BTR-STV."
> >
> > Actually, neither RP nor Schulze has better Condorcet efficiency than
> > Smith//TopTwoRunOff, which is the simple method you should be aiming for.
>
> Of course the Condorcet efficiency is the same, however the compromise
> incentive
> (or other incentives) won't be, across various methods.
>
> What hurts my heart is if we will say "let's adopt Condorcet, so people
> don't
> have to always vote for the lesser evil, and weak candidates won't spoil
> races,
> etc." and then we leave so much of this promise on the table unused.
>
> I just ran some 4-candidate 5-bloc no-ER random sims. I don't do exhaustive
> searches so take these numbers as suggestive only (not even
> minimums/maximums).
>
> Compromise incentive detected in what % of elections sans majority
> favorite:
> 3.0% best achieved by an experimental method
> 4.0% River, Schulze(WV), MAM
> 4.4% MinMax(WV)
> 4.6% BTP
> 10.2% MinMax(margins)
> 12.0% Bucklin
> 13.2% Condorcet//Approval (implicit)
> 14.6% FPCC (an extension of Stensholt BPW)
> 15.3% Condorcet//King of the Hill
> 17.2% TACC (implicit)
> 17.8% Condorcet//FPP
> 18.1% Condorcet//IRV and my extension of Kristofer's Linear method (tie)
> 18.3% BTR-IRV
> 26.5% IRV
> 40.4% FPP
>
> To be fair, I am running the same ballots through every method, which may
> not
> be realistic. These numbers can also differ if you generate scenarios
> based on
> an underlying issue space. But aside from these points, I can't help but
> notice
> that a lot of these "strategy-resistant" Condorcet methods are getting
> beat by
> Bucklin.
>
> Of course, Bucklin's Condorcet efficiency is really poor, and the
> truncation
> incentive is horrendous. But what's the goal of Condorcet efficiency, is
> it an
> end in itself? Personally I'm not comfortable thinking of it that way
> (maybe
> because it's defined on the cast ballots only, which seems insufficiently
> grounded in the underlying preferences which are what really matter).
>

I agree completely. All Condorcet methods elect ballot Condorcet candidates
(when they exist) 100% of the time by definition.

Now which methods will elect the sincere CW candidate C, when the sincere
(not ballot) preferences are given by

40 A>C
35 B>C
25 C>A

???

Answer: The methods that are known to automatically backfire on an A
faction burial of C under B.

TACC is such a method. If it is the official method, and word gets around
that burial doesn't pay under TACC, then there will be no burial, so C will
be elected.

But if the official method is Shulze, RP, MinMax, or any other method that
breaks a cycle at its weakest defeat ... that method may very well elect A,
depending on how opportunistic the A faction is.

If the A faction buries the sincere CW under B, and the majority that
prefers C over A takes no deliberate counter measure, then A will win.

To me, this means that effectively TACC has greater Condorcet efficiency
than any of the highly vaunted Condorcet methods.

Their problem is that their design is based on Condorcet's quaint heuristic
of setting out to correct mistaken opinions or "propositions," as opposed
to guarding against intentional gaming of the method.

"The opinion of a larger majority is more likely to be correct than that of
a smaller majority." ... in other words, a naïve statistical heuristic
versus a realistic game theoretic guide.

A cycle that was created intentionally is treated as though it was an
innocent error to be corrected by an information theoretic/statistical
approach. "The weakest link is the proposition least likely to be correct."

Trying to divine the true message from an intentionally garbled signal is
like trying to put humpty-dumpty back together... the proverbial highly
fraught cure (ambulance at the bottom of the ckiff) instead of prevention
(guard rail at the top).

Crime shouldn't pay! Even though most people are honest, let's observe the
wisdom of the anti-fragility design principle!

The Quick & Dirty/Clean version of TACC is a simple, transparent method
that holds up to this robust design principle:

Elect the most approved candidate not defeated pairwise by the least
implicitly approved Smith candidate.

(So the elected candidate is not the one responsible for the low implicit
approval of the presumed burial victim.)

What about the possibility of a sincere cycle where the Condorcet/Eppley
heuristic is actually relevant?

The highest approval candidate not beaten by the weakest Smith candidate
has to be a Smith candidate itself .. no small achievement ... and can
respond to a complaint from an higher approval Smith candidate, "At least I
was not beaten pairwise by the weak approval candidate that beat you!"

So taking into account its monotonicity and at least marginal clone
independence (no worse than Approval's), this Q&D/C method seems fairly
promising in the class of Universal Domain methods ... so far, so good!




>
> I haven't tried to do an extensive study of the burial games possible under
> Condorcet//FPP. But measuring similarity of results with three candidates,
> the
> three most similar methods are BTR-IRV (literally the same method),
> Kristofer's
> Linear method, and a bit further away, Condorcet//IRV.
>
> 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."
>
> Incidentally, if you want a Condorcet method where burial never looks
> attractive
> in the first place (before even considering strategic responses to
> burial), the
> best methods I have are Stensholt's (SV and BPW slash FPCC), C//IRV, and
> C//KOTH.
> None are monotone though.
>
> Kevin
>
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