<html><head></head><body><div class="ydpe918c6a6yahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:16px;"><div></div>
<div><div><div>Hi John,</div><div><br></div><div>We've discussed MMPO a lot in past years. Its main advantage is not just LNHarm,</div><div>but also FBC (favorite betrayal). (Kristofer mentions Participation, but I think</div><div>he may have DSC in mind there.)</div><div><br></div><div>I think I agree with Kristofer at least in that, if you modify the method such</div><div>that you break compliance with the criteria, you'll have the burden of showing</div><div>that the method still performs better than average according to your metric. And</div><div>you have to keep people's attention long enough to make the case.</div><div><br></div><div>I can't think of too many efforts I made to "fix" MMPO while salvaging LNHarm.</div><div>The closest I can think of is my idea to use MMPO to choose the winner from</div><div>Woodall's CDTT, which is the Schwartz set defined using only the majority-strength</div><div>pairwise contests. This set is more LNHarm-friendly (basically because it is less</div><div>responsive to changes in the matrix), but remains incompatible with LNHarm given</div><div>4+ candidates. The combined method also doesn't satisfy Plurality. Off the top of</div><div>my head all it really does is fix the standard MinMax Clone-Winner failure</div><div>scenario.</div><div><br></div><div>There is tension between Plurality, LNHarm, and respecting pairwise majorities.</div><div>If you secure the first two and weaken the third, you'll probably end up with</div><div>something that isn't quite satisfying from a Condorcet perspective.</div><div><br></div><div>I'll mention a couple other ranked LNHarm methods. There's Woodall's Descending</div><div>Solid Coalitions (DSC) which satisfies Participation and also clone independence.</div><div>Your ranked ballot is basically translated into votes for each set of candidates</div><div>you prefer over every candidate ranked lower. Then there's a Tideman-like</div><div>procedure to lock results. You can easily make your vote useless if you have an</div><div>unusual preference order. This gives it a strange burial strategy (technically)</div><div>that resembles responding to the incentives of a chicken dilemma criterion.</div><div><br></div><div>I made a LNHarm method that I called Quick Runoff (QR) or Chain Runoff. I think</div><div>Chain Runoff is a more evocative name now. Sort the candidates by first</div><div>preference count. (You can't equal rank.) You examine the pairwise contest</div><div>between each adjacent pair of candidates, starting at the top and going down. But</div><div>you stop as soon as the lower-ranked (i.e. fewer first preferences) candidate</div><div>does not have a full majority (i.e. of all voters) win over his opponent. That</div><div>opponent is elected.</div><div><br></div><div>(Equivalently, elect the candidate with the most first preferences who both has a</div><div>majority-strength win over the candidate ranked above him (or has no such</div><div>candidate), and also does not have a majority-strength loss to the candidate</div><div>ranked beneath him (or has no such candidate).)</div><div><br></div><div>This satisfies LNHarm because adding a new lower preference A>B can only have an</div><div>effect if B is currently the winner. It satisfies Plurality since the winner of</div><div>the method is either the first preference winner, or else has a majority-strength</div><div>pairwise win over somebody (meaning only a majority favorite could disqualify</div><div>them). On the negative side, there is a monotonicity issue in that a losing</div><div>candidate can wish they had received fewer first preferences, as it would have</div><div>given them more advantageous match-ups.</div><div><br></div><div>Just a few comments on the topic.</div><div><br></div><div>Kevin</div><div><br></div></div><br></div><div><br></div>
</div><div id="ydp22d06551yahoo_quoted_4761210310" class="ydp22d06551yahoo_quoted">
<div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;">
<div>
Le dimanche 1 novembre 2020 à 23:51:13 UTC−6, John Karr <brainbuz@brainbuz.org> a écrit :
</div>
<div><br></div>
<div><br></div>
<div><div dir="ltr">I've seen very little written about the MinMax Pairwise Opposition <br></div><div dir="ltr">Method. Which is surprising, given that it is the only Later Harm Safe <br></div><div dir="ltr">RCV method other than IRV (that I'm aware of).<br></div><div dir="ltr"><br></div><div dir="ltr">It counts the votes against each choice and elects the choice that had <br></div><div dir="ltr">the lowest opposition in its worst pairing.<br></div><div dir="ltr"><br></div><div dir="ltr">It appears to agree with Condorcet more often than IRV does and handle <br></div><div dir="ltr">Clones much better than IRV. Its' weakness is that it fails the <br></div><div dir="ltr">Plurality and Condorcet Loser Criterion.<br></div><div dir="ltr"><br></div><div dir="ltr">The obvious fixes involve pairing it with other methods such as <br></div><div dir="ltr">restricting it to Smith Set when there is no Condorcet Winner (only <br></div><div dir="ltr">helpful when there is no Condorcet Winner) or having a Runoff of the IRV <br></div><div dir="ltr">Winner vs the MMPO winner, both of which introduce some later harm <br></div><div dir="ltr">potential. Or alternately Dropping all choices lower in approval than <br></div><div dir="ltr">the first choice votes for the plurality leader (while fixing Plurality <br></div><div dir="ltr">it does not guarantee to eliminate the Condorcet loser) also introduces <br></div><div dir="ltr">a later harm concern.<br></div><div dir="ltr"><br></div><div dir="ltr"><br></div><div dir="ltr"><br></div><div dir="ltr">----<br></div><div dir="ltr">Election-Methods mailing list - see <a href="https://electorama.com/em " rel="nofollow" target="_blank">https://electorama.com/em </a>for list info<br></div></div>
</div>
</div></body></html>