[EM] Best IRV Tweak

[Susan Simmons]

Yes, Kristofer, specifically it is Benham's "Raynaud(Gross Loser)" the version of Reynaud that Chris Benham devised to satisfy Plurality.

Let's call it BRGL to avoid the question of Reynaud versus Raynaud.

BRGL succinctly stated: until only one candidate remains the loser of the (remaining) pairwise contest with the fewest losing votes is eliminated.

As Daniel noted, this is much simpler and cleaner (at least computationally) than the "BTR" patched version of IRV. And yet, from one point of view, it only differs from IRV on the question of which remaining candidate at each step is to be deemed "weakest" ... the Plurality loser or the pairwise loser with the least support.

To see that BRGL is an ISDA method, consider that no matter the order of elimination of the candidates up to any stage of the process, the next Smith candidate to be eliminated will be due to its defeat by the other remaining Smith member against which it musters the fewest votes.

VoteFair points out that IPE is similar to BRGL and probably superior to BRDL in simulations. But IPE lacks the clean simplicity of BRDL, espcially when IPE is hybridized with the BTR patch, as proposed by VoteFair.

It's proabably too late for Robert B-J to shift from BTR-IRV to BRDL in his presentation in Burlington, and not necessary, because his main point is that a conceptually and operationally small tweak of IRV totally fixes IRV's lack of Condorcet compliance. In fact, as suggested by "Robla," he should forget BTR and just graft a Condorcet check onto the front of IRV. [From there it's an easy future step to check for a CW among the remaining candidates at each round of the instant runoff ... a frequent proposal on the EM list].

Forest

(from my wife's phone)



Sent from my MetroPCS 4G LTE Android Device


-------- Original message --------
From: Kristofer Munsterhjelm <km_elmet at t-online.de>
Date: 7/7/21 8:26 AM (GMT-08:00)
To: Susan Simmons <suzerainsimmons at outlook.com>, election-methods at lists.electorama.com
Subject: Re: [EM] Best IRV Tweak

On 06.07.2021 20:59, Susan Simmons wrote:
>
> While there remains more than one uneliminated candidate eliminate the
> remaining one that is weakest relative to the other remaining candidates.
>
> If "weakest" means least top support (relative to the other remaining
> candidates) then we have IRV.
>
> But if we interpret "weakest" to mean the candidate with the fewest
> votes in any head-to-head contest (among the remaining candidates) then
> we have a Condorcet Compliant method.
>
> In fact, the weakest candidate in this sense is a pairwise loser to its
> opponent in its worst head-to-head contest ... which could not happen to
> a Condorcet Candidate.

That sounds like Raynaud, which is Minmax-elimination.

More information here: https://electowiki.org/wiki/Raynaud

-km
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