[EM] Agenda Based Banks

[Susan Simmons]

Great explanatory insight!



Sent from my MetroPCS 4G LTE Android Device


-------- Mensaje original --------
De: Kristofer Munsterhjelm <km_elmet at t-online.de>
Fecha: 2/8/21 2:13 p. m. (GMT-08:00)
A: Susan Simmons <suzerainsimmons at outlook.com>, election-methods at lists.electorama.com
Asunto: Re: [EM] Agenda Based Banks

On 02.08.2021 21:31, Susan Simmons wrote:
> It turns out that this method as it stands is not monotonic, but if you
> omit the downward part, then the remaining simpler version is monotonic:
>
> First initialize a set named "TheBank" with the most promising agenda item.
>
> Then, as long as even one agenda item pairwise beats every member
> ofTheBank, deposit the least promising of these into TheBank.
>
> Elect the final deposit.
>
> This simple Banks compliant method is a generalization of TACC (Total
> Approval Chain Climbing).
>
> The only thing I don't like about it is that even when the most
> promising agenda item is in the Banks set, as likely as not it will
> elect a different member of that set. My tweak was designed to overcome
> that "defect" while preserving Banks efficiency. But it's not worth the
> loss of monotonicity.
>
> Furthermore, it may turn out that the supposed "defect" actually confers
> burial resistance ... for example ...
>
> 45 A>B (sincere A>C)
> 25 B>C
> 30 C>A
>
> Ballot pairwise beat cycle: A>B>C>A
>
> Agenda: C<B<A
> (based on implicit approval, for example)

That feels like it's a general feature. Consider e.g. Benham with a
preset ordering as an agenda method (remove the loser until there's a CW
among the remaining candidates). Then raising W puts more candidates
between W and the end of the list, which means that in the worst case,
more candidates have to be eliminated before W wins.

It seems like there's some kind of tension where, on the one hand, being
ranked more highly should be advantageous (which it is if the pairwise
preferences don't change, because it saves W from early elimination),
but on the other hand, being ranked more highly with pairwise
preferences changing has a higher chance of being detrimental (because
more candidates have to be eliminated before W becomes a CW).

-km
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