[EM] Preliminary Chain Climbing investigation

[Forest Simmons]

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.

On Sun, Aug 13, 2023, 10:04 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> So I implemented chain climbing as a higher order/meta method in
> quadelect to check if it is compatible with or can improve strategy
> resistance. What I've found so far (assuming my implementation is
> correct) is:
>
> - Strategy resistant methods don't seem to preserve their resistance
> when used as the base method for chain climbing (starting from loser and
> then building a chain).
>
> - At least for three candidates, where I have brute-force methods, there
> do exist base methods whose compositions with chain climbing are
> strategy resistant.
>
> - However, these base methods make absolutely no sense on their own.
>
> So the pattern seems to be that while chain climbing ensures Banks
> compliance, it nonlinearly warps the landscape of which methods are good
> and which are bad, which means that our usual heuristics won't work. It
> becomes very difficult to create a method that preserves desirable
> properties when passed through chain climbing.
>
> As an example of strange base methods, here's a linear three-candidate
> method in the format of fpA-fpC:
>
> f(A) = BAC + 2 BCA - ABC
>
> The composition of this and chain climbing has about the same strategy
> resistance as Smith,IRV. And here's a nonlinear method:
>
> f(A) = BCA * BAC
>
> with similar performance as fpA - fpC. Neither of these strange methods
> is monotone.
>
> On a more theoretical level, it should be possible to craft a base
> method so that the chain climbing composition always produces the same
> winner as fpA-fpC in the three candidate case, by building a set of
> implications. E.g. let f(A) = fpA - fpC be the method we want to
> replicate, and g(A) be the scoring function for the base method we want
> to pass through chain climbing, then we have
>      whenever f(A) > f(B) > f(C) (i.e. A wins)
>      then either
>          g(C) > g(A) > g(B) or
>         g(A) > g(C) > g(B)
>
> and then similarly for every way to relabel candidates.
>
> In the first case, B is admitted, then A beats B pairwise and is
> admitted, then C isn't because C doesn't beat B; in the second case, B
> is admitted, then C is skipped, then A is admitted.
>
> But it's not a particularly pleasant way to design a method!
>
> -km
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20230814/039b3885/attachment.htm>