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Example of "Vindication":</div>
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11 A>B</div>
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15 C>A</div>
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7 B>C</div>
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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.</div>
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If the 7 B>C voters changed their votes to C>B (Favorite Betrayal), C wins.</div>
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If the 7 B>C voters don't vote at all C wins (participation failure).</div>
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If the 15 C>A voters vote C>B instead (Burial), C wins.<br>
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Sounds fishy to me, though there's probably something I'm missing. There usually is.</div>
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Jim Faran<br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Election-Methods <election-methods-bounces@lists.electorama.com> on behalf of Forest Simmons <forest.simmons21@gmail.com><br>
<b>Sent:</b> Friday, September 8, 2023 8:17 PM<br>
<b>To:</b> Kristofer Munsterhjelm <km_elmet@t-online.de>; EM <Election-methods@lists.electorama.com><br>
<b>Subject:</b> Re: [EM] Vindication</font>
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<div>A slightly simpler version for everyday citizens:</div>
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<div dir="auto">When there is no candidate with more than half of the first rank votes ...</div>
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<div dir="auto">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.</div>
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<div dir="auto">2. Eliminate Y after replacing all of Y's first rank ballot appearances with X.</div>
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<div dir="auto">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.</div>
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<div dir="auto">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).</div>
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<div dir="auto">fws</div>
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<div dir="ltr" class="x_gmail_attr">On Fri, Sep 8, 2023, 10:56 AM Forest Simmons <<a href="mailto:forest.simmons21@gmail.com">forest.simmons21@gmail.com</a>> wrote:<br>
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<div dir="auto">Kristofer,
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<div dir="auto">This elimination method helps to explain the "unreasonable effectiveness" of what we have been calling Max X>Y.</div>
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<div dir="auto">While there remains no unbeaten candidate among the uneliminated... "vindicate" the victor X and eliminate the loser Y in the strongest pairwise defeat.</div>
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<div dir="auto">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.</div>
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<div dir="auto">We say "misguidedly" because X was already ranked above or equal to Y on the greatest majority of ballots.</div>
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<div dir="auto">So vindication is a new kind of vote transfer that applies when the strongest (remaining) defeat brings about the elimination.</div>
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<div dir="auto">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.</div>
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<div dir="auto">Example</div>
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<div dir="auto">49 C</div>
<div dir="auto">26 A>B</div>
<div dir="auto">25 B</div>
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<div dir="auto">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.</div>
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<div dir="auto">Vindication updates the ballot profile as</div>
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<div dir="auto">49 C</div>
<div dir="auto">26 C>B</div>
<div dir="auto">25 B</div>
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<div dir="auto">So C now defeats B 75 to 25!</div>
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<div dir="auto">Try this out on your favorite ballot profiles, and see if you like it.</div>
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<div dir="auto">fws</div>
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