[EM] Vindication

[James Faran]

Example of "Vindication":

11 A>B
15 C>A
 7 B>C

A>B by 26-7 is the strongest win, so B is eliminated and the 7 B>C votes become A>C votes and A wins over C 18-11.

If the 7 B>C voters changed their votes to C>B (Favorite Betrayal), C wins.
If the 7 B>C voters don't vote at all C wins (participation failure).
If the 15 C>A voters vote C>B instead (Burial), C wins.

Sounds fishy to me, though there's probably something I'm missing.  There usually is.
Jim Faran
________________________________
From: Election-Methods <election-methods-bounces at lists.electorama.com> on behalf of Forest Simmons <forest.simmons21 at gmail.com>
Sent: Friday, September 8, 2023 8:17 PM
To: Kristofer Munsterhjelm <km_elmet at t-online.de>; EM <Election-methods at lists.electorama.com>
Subject: Re: [EM] Vindication

A slightly simpler version for everyday citizens:

When there is no candidate with more than half of the first rank votes ...

1.Find the candidate X that has the strongest head-to-head victory over any other candidate Y. This means (i) that X outranks Y on more ballots than Y outranks X, and (ii) that the number of ballots on which X outranks Y, plus the number of ballots on which Y out ranks no other candidate, is larger than the corresponding sum for any other pair of candidates.

2. Eliminate Y after replacing all of Y's first rank ballot appearances with X.

3. After these two steps if there is still no candidate with more than half of the first place votes, repeat steps (1) and (2) among the uneliminated candidates, until only one candidate remains.

Note that in each elimination stage the votes of the most strongly defeated loser are transferred to the winner of that maximal strength defeat. We call this kind of vote transfer, "vindication" (of the winner).

fws



On Fri, Sep 8, 2023, 10:56 AM Forest Simmons <forest.simmons21 at gmail.com<mailto:forest.simmons21 at gmail.com>> wrote:
Kristofer,

This elimination method helps to explain the "unreasonable effectiveness" of what we have been calling Max X>Y.

While there remains no unbeaten candidate among the uneliminated... "vindicate" the victor X and eliminate the loser Y in the strongest pairwise defeat.

Vindication of X is executed by raising X to the level of Y on any ballot that (misguidedly) ranked Y above X, before eliminating Y.

We say "misguidedly" because X was already ranked above or equal to Y on the greatest majority of ballots.

So vindication is a new kind of vote transfer that applies when the strongest (remaining) defeat brings about the elimination.

In the case of three candidates, that kind of vote transfer will be sufficient to turn X into a majority winner ... and in general, will likely change the strongest victor into an undefeated candidate.

Example

49 C
26 A>B
25 B

If we measure defeat strength by Winning Votes + Losing Truncations, we see that the defeat of A by C is strongest: WV+LT = 49+74 = 123.

Vindication updates the ballot profile as

49 C
26 C>B
25 B

So C now defeats B 75 to 25!

Try this out on your favorite ballot profiles, and see if you like it.

fws
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