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<div>Hi Forest, I agree your revision seems better. I also don't like the potential for C3 to change the outcome like that.</div><div><br></div><div>It seems like the revised method would usually elect C1, with the most common exception being when C2 pairwise defeats C1. As you proceed down the list it starts to become hard to imagine how the candidate could do well enough in pairwise contests (to be elected) while doing so poorly in approval.</div><div><br></div><div>So this seems to me like a clone-independent way of fixing an overly simple method like "elect the approval winner unless second place beats him pairwise."</div><div><br></div><div>Kevin</div><div><br></div></div><blockquote style="margin: 0 0 0 40px; border: none; padding: 0px;"><div class="ydp6221a3f1yahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:16px;"><div><br></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div>
Le samedi 2 mars 2019 à 15:20:39 UTC−6, Forest Simmons <fsimmons@pcc.edu> a écrit :
</div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><br></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><br></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>A few years back Jobst suggested "chain climbing" as a seamless, Condorcet compliant way of selecting an alternative from a given ordered list.</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>For example electing a winner from a list of candidates c1, c2, ... given in decreasing order of approval.</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>Chain Climbing initializes a chain of candidates with the last (least approved in this case) candidate in the list. Then moving up the list each successive candidate "climbs the chain" as far it can before being bumped off by a chain member that defeats it. If it makes it all of the way to the top, it is added to the top of the chain.</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>The candidate who ends up at the top of the chain is elected.</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>Since a beats all candidate will never be defeated, the method is Condorcet compliant. It also turns out to be clone resistant and monotonic. </div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>Another nice property is that it always selects from the Banks set, a nice game theoretic subset set of the set of uncovered candidates. </div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>The biggest objection to this method is that when applied to a list a list where c1 beats c2 beats c3, and c3 beats c1, it elects c2. </div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>Here's my proposed improvement:</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>Initialize the chain with c1. Move down the list instead of up. For each successive candidate x (as we move down the list) if possible, insert that candidate into the chain at a point where it is beaten by every candidate above it and is not defeated by any candidate below it. If not possible, discard it.</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>After going through the entire list (top to bottom) inserting new candidates where possible into the totally ordered chain, we end up with a maximal totally ordered chain of candidates (ordered by pairwise defeat) The candidate at the top fo the completed chain (the one who is not defeated by any of the others) is elected.</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>It is easy to show that this method has all of the nice properties of chain climbing, but retains more of the spirit of the original list..</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>For example in the A>B>C example above it elects A.</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>What do you think?</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div>Forest</div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div><div id="ydp1f1c1826yiv6443967239"><div dir="ltr"><div><br></div></div></div></div></div></div></blockquote><div id="ydp1f1c1826yahoo_quoted_1715670866" class="ydp1f1c1826yahoo_quoted">
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