[EM] Preliminary Chain Climbing investigation

[Forest Simmons]

On Wed, Aug 16, 2023, 4:39 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 8/15/23 03:20, Forest Simmons wrote:
> > As soon as you abandon the monotone agenda formation requirement, chain
> > Climbing (from the nominally unpromising end of the agenda towards the
> > nominally favorable end) loses its validity ... all bets are off.
> >
> > In the three candidate Smith set case the most promising candidate that
> > defeats the least promising Smith member is elected.
> >
> > The least promising Smith member is usually the sincere CW. The Smith
> > member that beats it is the "bus" under which it was nuried ... so good
> > poetic punishment for the niriers.
> >
> > Like most methods good at punishing the buriers, this method needs a
> > sincere runoff to recover the sincere CW.
> >
> > The appropriate three candidate runoff is the chain climbing winner W
> > [most likely the bus] versus a runoff between the least promising Smith
> > member Z [probably the sincere CW] and the one that does not defeat Z
> > [the probable burier candidate].
> >
> > Rational voters informed on preferences will pass on W, and elect Z.
> >
> > Any Condorcet method that almost always positively punishes the buriers
> > (by electing the "bus"rather than either the buried CW or burier) will
> > look just as strange. In particular it will fail symmetry reversal when
> > restricted to a three member Smith set.  Hence the importance of the
> > sincere runoff for any such method, not just chain climbing.
>
> That's not quite what I'm saying. The candidate who is elected by a
> burial-resistant method may leave something to be desired if burial is
> done anyway - see my other reply. But what seems to be particular to
> chain climbing - at least on agendas that aren't strongly monotone - is
> that it warps the regions where good methods lie and where the bad
> methods lie so thoroughly that nothing makes sense anymore.
>
> It's not just that strategy-resistant methods produce bad outcomes. But
> rather, methods that were originally strategy resistant stop being so;
> but methods that weren't strategy resistant don't gain resistance either.
>
> I ran the chain climbing composition of just about every method
> available to quadelect (some methods excluded due to bugs or
> neutrality/anonymity violations), using a multi-armed bandit search to
> find the best. The best "plain" strategy-resistant method is usually
> something like Smith,IRV or Smith//IRV where strategy succeeds around
> 45-50% of the time under impartial culture (97 voters, 5 candidates),
> disregarding Antiplurality whose results seem to just be an artifact of IC.
>
> With the chain climbing composition, the best methods are
> Antiplurality-CC and Coombs-CC, at 65% or so. And I suspect they only
> get that much because of impartial culture's weak spot to antiplurality,
> although I'm surprised that doesn't get warped away too.
>
> Then I did a three candidate search over 15k linear methods and 100k
> nonlinear ones on three candidates, showing that strategy resistance
> still exists, but the methods make no sense.
>
> So perhaps what we can say is, and what I wanted to say was:
>         - Chain climbing doesn't work on methods that aren't strongly
>                 monotone.
>         - For such methods, strategy resistance is neither improved
>                 nor preserved through composition.
>         - There do exist non-strongly-monotone methods that when
>                 composed with CC are strategy-resistant.
>         - However, designing them is near-impossible.
>
> Which I guess is what you implied by "all bets are off". I just don't
> think the need for a runoff is related to the bizarre behavior of chain
> climbing in particular.
>

Well, in the rare but not insignificant case of a sincere three member top
cycle,  wv Ranked Pairs would give a much, much better result than Chain
Climbing on the RP finish order, which will elect the candidate that is
defeated by the RP winner

But, if the cycle is not sincere, that candidate that is beaten by the RP
candidate is the only one whose election will punish the buriers.... and
that candidate is the only one that defeats the Smith  candidate member
that is lowest in the RP finish order ... i.e. that candidate is the Chain
Climbing winner.

It punishes well, but like other burial resistant methods, it fails to
correct the burial.

There is a kind of uncertainty principle here, the more surely the method
punishes the buriers, the less likely it will elect the buried sincere CW.

That's why the better a method punishes buriers, the more important to have
a sincere runoff.

If you have a method M like RP that works well with sincere cycles, a
sincere runoff of the form S1 vs ( S2 vs S3) where S1,S2,S3 are the first
three Smith members in the Method M finish order ... that runoff will elect
the sincere CW among those three if there is one, else it will
appropriately elect S1.

It seems that's about the best we can do with a simple deterministic single
seat method based on ranked choice ballots and a top three Smith manual
runoff.
fws




> -km
>
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