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It is my impression that all elimination methods are not monotonic, though I certainly can't prove that.</div>
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In this case, if I've understood it correctly, try</div>
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7 A>B>C</div>
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2 B>A>C</div>
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7 B>C>A</div>
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8 C>A>B</div>
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Pairwise we have a cycle: A>B>C>A, so FPC scores are A:9; B:8; C:7. Thus, the method eliminates C and A beats B and A wins.</div>
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Now suppose the two B>A>C voters increase their appreciation of A and vote A>B>C instead.</div>
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<span style="font-size: 12pt; background-color: rgb(255, 255, 255);" class="ContentPasted0">9 A>B>C</span></div>
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7 B>C>A</div>
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<span style="font-size: 12pt; background-color: rgb(255, 255, 255);" class="ContentPasted0">8 C>A>B</span></div>
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<span style="font-size: 12pt; background-color: rgb(255, 255, 255);" class="ContentPasted0">We've got the same pairwise cycle, but now A gets eliminated first and B wins.</span></div>
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<span style="font-size: 12pt; background-color: rgb(255, 255, 255);" class="ContentPasted0">Did I calculate correctly? Is this the type of monotonicity you were asking about?</span></div>
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<span style="font-size: 12pt; background-color: rgb(255, 255, 255);" class="ContentPasted0">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 Filip Ejlak <tersander@gmail.com><br>
<b>Sent:</b> Monday, April 17, 2023 12:19 PM<br>
<b>To:</b> election-methods@lists.electorama.com <election-methods@lists.electorama.com><br>
<b>Subject:</b> [EM] a simple, great ISDA-compliant method I've never seen mentioned</font>
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<div>Hello, everyone, new to the list here,</div>
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what I really like about First preference Copeland is that it implies a nice method for calculating a sort of "Condorcet score": just count 1st preferences of all candidates (including candidate X) that do not beat X pairwise. Although it is highly resistant
to burial, FPC is not cloneproof and fails ISDA.
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<div>However, there is an easy way to fix these two problems: just do sequential loser elimination using FPC score!
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<div>(And when there is a tie at the bottom, break it by applying the same method to the candidates involved in the tie and finding the loser.)<br>
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<div>This method could be named FPCE (First Preference Copeland Elimination) or ISCR (Instant Simmons-Copeland Runoff). It is cloneproof (because even if there are clones which hurt one another, eventually there is only one of them left) and ISDA-compliant
(because all candidates outside the Smith set get eliminated before any Smith set member is eliminated). I think its burial resistance might be weakened, though, as it fails DMTBR.</div>
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<div>Could anyone help with proving/disproving monotonicity, or even LIIA? I applied the method to the 5-candidate Smith set from the Wikipedia article about Schulze and there turned out to be an LIIA-compliant order: ADCEB. I'm curious if it was by accident
or not.</div>
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<div>Filip Ejlak</div>
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