[EM] Vindication

[Forest Simmons]

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>
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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