[EM] Best IRV Tweak

[Susan Simmons]

Actually BRGL = MaxMin Loser-Elimination.

The winner of MaxMin is the candidate whose Min pairwise support is maximal. The loser of MaxMin is the candidate whose Min pairwise support is minimal ... the very "Gross Loser" candidate that BRGL eliminates at each elimination step (from among the candidates not previously eliminated).

Standard Reynaud, by way of contrast is MinMax Loser-Elimination.

The winner of MinMax is tbe candidate whose max pairwise defeat is minimal. The loser of MinMax is the candidate whose max defeat is maximal ... the very candidste that standard Reynaud eliminates at each step (from among the candidates not previously eliminated).





Sent from my MetroPCS 4G LTE Android Device


-------- Original message --------
From: Daniel Carrera <dcarrera at gmail.com>
Date: 7/7/21 12:28 PM (GMT-08:00)
To: Susan Simmons <suzerainsimmons at outlook.com>
Cc: Kristofer Munsterhjelm <km_elmet at t-online.de>, election-methods at lists.electorama.com
Subject: Re: [EM] Best IRV Tweak


On Wed, Jul 7, 2021 at 2:11 PM Daniel Carrera <dcarrera at gmail.com<mailto:dcarrera at gmail.com>> wrote:


On Wed, Jul 7, 2021 at 12:11 PM Susan Simmons <suzerainsimmons at outlook.com<mailto:suzerainsimmons at outlook.com>> wrote:
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.

Can also be called "Maximin"... I think... To me it looks like a mirror of Minimax (using votes instead of margins): The winner is the candidate whose lowest number of votes is higher. Maybe there is a subtle difference that I haven't detected yet, BRGL = maximin. Though that's not how I would choose to explain it to the public. The usual definition is clearer, especially to someone who already knows IRV: "remove the candidate with fewest votes in any pairwise contest and repeat".

Ugh... after I hit "send" I realized that this is wrong. In an election where voters are not required to do a full ranking, it is possible that removing the candidate with the fewest votes 'X' also removes the pairwise contest with the next-lowest number of votes:

5 --- A > B
2 --- A > C
3 --- B > A
4 --- B > C
1 --- C > A
6 --- C > B

The "maximin" winner is B but the BRGL winner is A. So nevermind.

Daniel.
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