<div dir="auto">I agree with Kristofer about the cliff analogy and take it a little further ... are we going to say that because it will be needed only rarely we can settle for any old simple alternative?<div dir="auto"><br></div><div dir="auto">Even if there were no significantly better equally simple solution ... it would still be shameful engineering practice:</div><div dir="auto"><br></div><div dir="auto">"Boss I cannot give the green light to the Challenger until we fix that O-Ring problem."</div><div dir="auto"><br></div><div dir="auto">"But we have a deadline to keep ... and there is only a 0.4 percent chance the thing will cause a problem ... so far, so good ... just cross your fingers and sign here."</div><div dir="auto"><br></div><div dir="auto">Here's a simple, acceptable method that beats many elaborate Condorcet proposals including Copeland,Baldwin, Black, Nanson, MinMax, and many others. If it turned out that twenty percent of Condorcrt election had cycles in a certain odd ball electorate, it would still be a credible, upstanding choice.</div><div dir="auto"><br></div><div dir="auto">It has a natural segue from the simplest definition of a Condorcet Winner into what to do if there is no CW:</div><div dir="auto"><br></div><div dir="auto">A Condorcet Winner C is a candidate that is unbeaten pairwise. This means that for any other candidate X, the number of ballots on which C outranks X is greater than the number of ballots on which X outranks C.</div><div dir="auto"><br></div><div dir="auto">In other words, C has a positive margin of support compared to any other candidate X.</div><div dir="auto"><br></div><div dir="auto">If there is no candidate with a positive margin of support compared to every other candidate, then elect the candidate with the single greatest margin of support relative to any other candidate.</div><div dir="auto"><br></div><div dir="auto">Example:</div><div dir="auto"> </div><div dir="auto">48 C</div><div dir="auto">28 A>B</div><div dir="auto">24 B</div><div dir="auto"><br></div><div dir="auto">A's margin of support relative to B is</div><div dir="auto">28-24=4</div><div dir="auto"><br></div><div dir="auto">B's margin over C is 28+24 vs 48 or 52-48 which equals 4, the same as A's margin over B.</div><div dir="auto"><br></div><div dir="auto">C's margin over A is 48-28=20, which is greater than either of the other positive margins, so the Plurality winner C wins in this example.</div><div dir="auto"><br></div><div dir="auto">Example2.</div><div dir="auto"><br></div><div dir="auto">40 A>B</div><div dir="auto">35 B>C</div><div dir="auto">25 C</div><div dir="auto"><br></div><div dir="auto">A's margin over B is 40-35=5</div><div dir="auto">B's margin over C is 40+35-25=50</div><div dir="auto">C's margin over A is 25+35-40=20</div><div dir="auto"><br></div><div dir="auto">Candidate B is the max defeat margin winner with a max margin of 50.</div><div dir="auto"><br></div><div dir="auto">So this time it would have been an embarrassment to elect the Plurality winner A ... whose max support margin was a mere 5 votes, the least of all.</div><div dir="auto"><br></div><div dir="auto">So can we agree to elect the candidate with the max fefest margin when there is no candidate with all positive margins?</div><div dir="auto"><br></div><div dir="auto">-Forest</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Feb 18, 2023, 3:47 AM Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de">km_elmet@t-online.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">On 2/18/23 10:42, Colin Champion wrote:<br>
<br>
> But then I don't favour Kristofer's proposal either. My evaluation <br>
> suggests that burial is a particular threat for Condorcet methods, and <br>
> that in its presence their accuracies are: minimax 64%, condorcet+fptp <br>
> 59%, copeland,fptp 48%. [Usual disclaimers apply.]<br>
<br>
That's fair; I was simply trying to find a minimal change to the method <br>
that would at least grant Smith or something like it.<br>
<br>
Really, what I'm concerned about is that there's such a, for lack of a <br>
better term, steep cliff from the Condorcet domain down to the Plurality <br>
domain. So everything's nice as long as you play on top of the mountain, <br>
but if you misstep (i.e. produce a cycle), then you don't gradually <br>
degrade, you fall directly into plain old Plurality, with all of its <br>
vote splitting problems. The discontinuity seems like something that's <br>
just asking to be exploited.<br>
<br>
Do you know of any alternate "bang for the buck" methods that would be <br>
simple enough to be accepted?<br>
<br>
-km<br>
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</blockquote></div>