[EM] Making any method DH3-proof

Forest Simmons forest.simmons21 at gmail.com
Mon Jul 25 16:29:55 PDT 2022


I see ... the only reason you cannot dispense with the runoff step whenever
the two methods have the same winner, is to make sure the sincere Condorcet
loser never gets elected ... right?

But perhaps the runoff could be dispensed with if both methods yielded the
same winner AND this common winner had more than fifty percent first place
votes.

Would more than 50 percent implicit approval for the common winner of the
two methods be enough for such a runoff exemption?

El lun., 25 de jul. de 2022 3:26 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> As either I or Forest once mentioned, his honest runoff mechanism
> prevents the election of an honest Condorcet loser.
>
> It can therefore be used to stop any method from electing an universally
> despised dark horse if the runoff candidates are picked in such a way
> that at least one of them cannot be the/a dark horse.
>
> So here's a proof of concept:
>
> Let the voters rank the candidates twice. One of these rankings is
> marked "honest" and will only be used to resolve a runoff. On the other
> (say the one marked "ordinary"), they may strategize as much as they
> desire.
>
> Choose, for the virtual runoff, the winner of some base method using the
> O (ordinary) ballots, and the Plurality (or IRV) winner using the same
> ballots. If this elects the same candidate, pick the second place
> Plurality (or IRV, etc) finisher as the other finalist, instead.
>
> Finally, elect the one that beats the other pairwise according to the H
> ballots.
>
>
> Now, an objection of mine is that this kind of ballot format may seem
> ridiculous or bizarre. "Why do I have to fill in my ballot twice? And
> how do I know that I can be honest on the H ballot?". If so, just do an
> ordinary runoff instead of using Forest's virtual runoff. (Sophisticated
> game theory arguments don't help if the voters don't believe them.)
>
> If that ordinary runoff has a debate period where the voters can more
> thoroughly scrutinize the candidates (through the media), then it would
> also help distinguish weak centrists from strong winners, if that's
> deemed to be a problem with the base method. (E.g. people who don't like
> Condorcet often say its problem is that it elects weak candidates too
> often.)
>
>
> So in short: if you use a Forest or real runoff between the winner of
> any method and the highest placed different winner of a method that
> isn't susceptible to DH3, then the combined method isn't either.
>
> -km
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>
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