<html><head></head><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px"><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><font size="3" id="yui_3_16_0_ym19_1_1478812956738_60070">Ok. I notice from your description that it's not clear how to decide whether a different method would satisfy the weak IIA. It seems like it will be really hard to define it, because your definition of the second "relevant" candidate is very specific to this method.</font></div><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><font size="3"><br></font></div><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><font size="3" id="yui_3_16_0_ym19_1_1478812956738_60407">Incidentally I feel even the methods that fully satisfy the letter of IIA don't seem to do anything of value stemming from that fact. E.g. we expect real Approval voters to generally approve at least one and disapprove at least one candidate of those offered. But that assumption already means we can't safely delete losers without fear of changing the winner.</font></div><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><font size="3"><br></font></div><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><font size="3" id="yui_3_16_0_ym19_1_1478812956738_60892">I'm not too optimistic about Participation, either, as all the (non-random?) methods that satisfy it just sum points. DAC and DSC seem like the upper limit of complexity so far, and they are not that great.</font></div><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><font size="3"><br></font></div><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1478812956738_61095">My take on the general concept of TTAPR is to start by checking for a majority favorite, and then have the pairwise comparison between the two candidates who minimize the number of voters who didn't approve either of them. But that rule could exclude the approval winner from the comparison. A different option could be to compare the approval winner with the candidate most approved on ballots not approving the approval winner. (We've called this measure "approval opposition" I believe.)</span><br></div><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><span style="font-size: medium;"><br></span></div><div id="yui_3_16_0_ym19_1_1478812956738_59338" dir="ltr"><span style="font-size: medium;">Kevin</span></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1478812956738_59330"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1478812956738_59334" style="display: block;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12px;" id="yui_3_16_0_ym19_1_1478812956738_59333"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_ym19_1_1478812956738_59332"> <div dir="ltr" id="yui_3_16_0_ym19_1_1478812956738_59331"> <font size="2" face="Arial" id="yui_3_16_0_ym19_1_1478812956738_59952"> <hr size="1" id="yui_3_16_0_ym19_1_1478812956738_59951"> <b><span style="font-weight:bold;">De :</span></b> Monkey Puzzle <araucaria.araucana@gmail.com><br> <b><span style="font-weight: bold;">À :</span></b> Kevin Venzke <stepjak@yahoo.fr> <br><b><span style="font-weight: bold;">Cc :</span></b> EM <election-methods@lists.electorama.com><br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Jeudi 10 novembre 2016 17h16<br> <b><span style="font-weight: bold;">Objet :</span></b> Re: [EM] Top-two Approval Pairwise Runoff (TTAPR)<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1478812956738_59360"><br><div id="yiv6959377606"><div id="yui_3_16_0_ym19_1_1478812956738_59362"><div dir="ltr" id="yui_3_16_0_ym19_1_1478812956738_59361">Thank you for your reply, Kevin. It is nice to get clarification on an 11-year-old thread :-).<div id="yui_3_16_0_ym19_1_1478812956738_59363"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59364">If you have by now seen subsequent replies, you will note that Jameson Quinn proposed a refinement which I think might be better than the original method. Call it Reweighted Approval Pairwise (RAP) to avoid potentially derogatory acronyms:</div><div id="yui_3_16_0_ym19_1_1478812956738_59365"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59366">Graded ballots with approval cutoff (A > B > C approved > D disapproved > E > F).</div><div id="yui_3_16_0_ym19_1_1478812956738_59370"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59371">Pick approval winner X for first runoff seat.</div><div id="yui_3_16_0_ym19_1_1478812956738_59372"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59373">Reweight all X-approving ballots by <span style="color:rgb(0,0,0);font-size:12.8px;" id="yui_3_16_0_ym19_1_1478812956738_59515">1/2 (D'Hondt) or 1/3 (Sainte-Laguë) [at the moment I'm leaning toward 1/2].<br clear="none"><br clear="none">Pick reweighted approval winner Y for second runoff seat.</span></div><div id="yui_3_16_0_ym19_1_1478812956738_59374"><span style="color:rgb(0,0,0);font-size:12.8px;"><br clear="none"></span></div>Kristofer Munsterhjelm noted that a second n^2 array could be accumulated summably at the same time as the pairwise array to assist in the Y choice.<div id="yui_3_16_0_ym19_1_1478812956738_59485"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59383">The winner is the pairwise winner (PW) of X vs. Y. Call the pairwise loser PL.</div><div id="yui_3_16_0_ym19_1_1478812956738_59379"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59484">Adding any ballot that approves PW but does not approve PL should only add to PW's approval or the PW>PL pairwise vote. So this ballot should never be eliminated by reweighted approval. The ballot increases or does not change PW vs. PL pairwise. Therefore this method meets a weak participation criterion.</div><div id="yui_3_16_0_ym19_1_1478812956738_59388"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59387">The method could fail strong participation if the additional ballot approved both PW and PL, causing one or the other to lose to a third candidate. However, I would argue that the clone independence conferred by reweighted approval voting would tend to discourage this in most cases.</div><div id="yui_3_16_0_ym19_1_1478812956738_59377"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59386">Similarly, I believe the method passes a weak IIA if the irrelevant candidate is neither X or Y. Most voters would consider even the pairwise loser to be relevant, in my opinion.</div><div id="yui_3_16_0_ym19_1_1478812956738_59385"><br clear="none"></div><div id="yui_3_16_0_ym19_1_1478812956738_59959">Ted</div></div><div class="yiv6959377606gmail_extra" id="yui_3_16_0_ym19_1_1478812956738_59492"><br clear="all"><div id="yui_3_16_0_ym19_1_1478812956738_59958"><div class="yiv6959377606gmail_signature" id="yui_3_16_0_ym19_1_1478812956738_59957"> Frango ut patefaciam -- I break so that I may reveal<br clear="none"></div></div>
<br clear="none"><div class="yiv6959377606yqt5900471329" id="yiv6959377606yqt48286"><div class="yiv6959377606gmail_quote" id="yui_3_16_0_ym19_1_1478812956738_59491">On Thu, Nov 10, 2016 at 2:21 PM, Kevin Venzke <span dir="ltr"><<a rel="nofollow" shape="rect" ymailto="mailto:stepjak@yahoo.fr" target="_blank" href="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</a>></span> wrote:<br clear="none"><blockquote class="yiv6959377606gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;" id="yui_3_16_0_ym19_1_1478812956738_59490"><div id="yui_3_16_0_ym19_1_1478812956738_59489"><div style="color:#000;background-color:#fff;font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px;" id="yui_3_16_0_ym19_1_1478812956738_59488"><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21156"><font id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_22155" size="3">Hello,</font></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20883"><font size="3"><br clear="none"></font></div><div dir="ltr" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20881"><font id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_22514" size="3">I'm mainly saying that (purely in theory) the runoff method shouldn't behave any differently from Approval (</font><span id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_22413" style="font-size:medium;">i.e. if the nominators know what they are doing and voters don't mind clones). I don't see an advantage to having the voters pick between two clones when (in theory, again) those clones wouldn't even be there, save for the incentives of the method. You could counter my criticism by saying a mechanism is allowed to be "theoretically" pointless if in practice it would be OK. Harder to sell such a method though, I think.</span></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20881"><font size="3"><br clear="none"></font></div><div dir="ltr" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20881"><font id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21070" size="3">The method doesn't satisfy Participation or IIA. Notice that deleting the loser of the final runoff does not necessarily preserve the original winner. And adding ballots that approve the winner can change who the winner is up against, making him lose.</font></div><div dir="ltr" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20881"><br clear="none"></div><div dir="ltr" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20881"><font color="#252525" face="sans-serif" size="3">Kevin</font></div><div class="yiv6959377606m_-6031846673893898544qtdSeparateBR" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20880"><br clear="none"><br clear="none"></div><div class="yiv6959377606m_-6031846673893898544yahoo_quoted" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20648" style="display:block;"> <div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20647" style="font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px;"> <div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20646" style="font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px;"> <div dir="ltr" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20879"> <font id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21161" size="2" face="Arial"> </font><hr id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21160" size="1"> <b><span style="font-weight:bold;">De :</span></b> Monkey Puzzle <<a rel="nofollow" shape="rect" ymailto="mailto:araucaria.araucana@gmail.com" target="_blank" href="mailto:araucaria.araucana@gmail.com">araucaria.araucana@gmail.com</a>><br clear="none"> <b><span style="font-weight:bold;">À :</span></b> EM <<a rel="nofollow" shape="rect" ymailto="mailto:election-methods@lists.electorama.com" target="_blank" href="mailto:election-methods@lists.electorama.com">election-methods@lists. electorama.com</a>> <br clear="none"> <b><span style="font-weight:bold;">Envoyé le :</span></b> Jeudi 10 novembre 2016 13h31<br clear="none"> <b><span style="font-weight:bold;">Objet :</span></b> [EM] Top-two Approval Pairwise Runoff (TTAPR)<br clear="none"> </div> <div class="yiv6959377606m_-6031846673893898544y_msg_container" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20645"><div><div class="yiv6959377606h5"><br clear="none"><div id="yiv6959377606m_-6031846673893898544yiv9480498278"><div dir="ltr" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20644">Back in 2005, Russ Paielli proposed the following to this list:<div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20643">(<a rel="nofollow" shape="rect" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20878" target="_blank" href="https://www.mail-archive.com/election-methods-electorama.com@electorama.com/msg06164.html">https://www.mail-archive.com/ election-methods-electorama. com@electorama.com/msg06164. html</a>)<br clear="none"><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20877"><br clear="none"></div><blockquote class="yiv6959377606m_-6031846673893898544yiv9480498278gmail_quote" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20642" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex;"><span style="font-size:15px;">I</span>'m up too late again, and I just had an interesting idea. If the<br clear="none">following method has been proposed before, please let me know.<br clear="none">The voters rank the candidates and specify an Approval cutoff. The<br clear="none">winner is then the pairwise winner of the top-two most-approved candidates.<br clear="none">If it doesn't have a name already, let me tentatively call it ATTPR for<br clear="none">Approval Top-Two Pairwise Runoff.<br clear="none">A simpler variation would be to let the voter rank only the approved<br clear="none">candidates, thereby eliminating the need for an explicit Approval cutoff.<br clear="none">Good night, or good morning, whichever the case may be.</blockquote><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20705"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20706">I'd like to revive this proposal, in the following form, still basically what Russ proposed:<br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20708"><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20707"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20709">Voters grade the candidates on a 6 level scale, A>B>C>D>E>F.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20710"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20823">Grades A, B, or C are approved; D, E, or F are disapproved.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20711"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20803">Rank preferences are inferred from ratings, and the pairwise winner of the top two approved candidates is the winner.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20712"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20802">I'd like to defend this method against the two objections posed at the time:</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20713"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20824">Kevin Venzke raised the following objection:</div><blockquote class="yiv6959377606m_-6031846673893898544yiv9480498278gmail_quote" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20825" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex;">This fails Clone-Loser pretty badly: if the faction commanding the most<br clear="none">approval runs two candidates, they can win regardless of the pairwise<br clear="none">comparison.</blockquote><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20714"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_20715">My take on this is that you would have the same problem with straight Approval. The full pairwise comparison ensures that the least objectionable of the clones (to both winning and losing factions) is the one who wins. Since my primary metric is finding the candidate who minimizes variance, there is better variance-minimizing when those disagreeing with the top-two approved candidates are able to have a voice in the comparison between the two.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21039"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21040">Chris Benham responded with the following objection:</div><blockquote class="yiv6959377606m_-6031846673893898544yiv9480498278gmail_quote" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21041" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex;">This would be a strategy farce. Voters who are only interested in<br clear="none">electing their favourite would all have incentive to approve, besides<br clear="none">their favourite, any and all candidates<br clear="none">that they think that their favourite can beat in the runoff. The net<br clear="none">effect of this strategising could be that that the two candidates in<br clear="none">the runoff could be the two *least* popular<br clear="none">(sincerely approved).<br clear="none">As well of course, as Kevin pointed out, well-resourced parties would<br clear="none">have incentive to each run two candidates to try to capture both runoff<br clear="none">spots.</blockquote><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21042"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21062">I disagree with the supposed strategic incentive. This seems to be a combination of pushover strategy plus Chicken Dilemma. The very fact that one might promote more than one sincerely disapproved candidate into the top-two set is itself a disincentive to the attempt, since you get only one coarse-grained shot at the top two. I think pairwise runoff is an incentive to avoid CD, but possibly not.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21061"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21060">And again, I'm not worried about a runoff between clones. The advantage of TTA is that if the larger faction is going to win anyway, the losing factions can at least have a voice in deciding the lesser of two evils.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21059"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21045">I'm primarily concerned about participation, monotonicity and independence from irrelevant alternatives. It seems to me that participation is satisfied as it would be with straight approval, since adding an approved vote for your favorite would never decrease approval, and adding a preference between favorite and any other compromise should never hurt either favorite or compromise. </div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21046"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21047">IIA seems like it should be satisfied because adding or removing a non-top-two candidate should never have an effect on the top-two pairwise comparison.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21048"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21049">The latter is interesting to me because one would expect that a method with ranking would fall under Arrow Impossibility conditions.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21050"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21051">It is apparent that TTAPR can fail Condorcet when the sincere CW is not in the top-two approved, but there is less chance of that occurring than would happen in simple Approval, so I see an improvement. Of course, it would still fail Smith and other full set Condorcet criteria also.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21058"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21052">In an ideal world, I would like to reduce the weight of the pairwise vote between two disapproved candidates, but in a USA-type election, it seems like one has to ensure that ballot weight is always 1 when making candidate comparisons to satisfy constitutional requirements.</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21053"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21054">Finally, I think this satisfies all the monotonicity criteria satisfied by Approval. Are there any counterexamples?</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21055"><br clear="none"></div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21056">Ted</div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21057">-- </div><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21439"><div id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21438"><div class="yiv6959377606m_-6031846673893898544yiv9480498278gmail_signature" id="yiv6959377606m_-6031846673893898544yui_3_16_0_ym19_1_1478812956738_21437"> Frango ut patefaciam -- I break so that I may reveal<br clear="none"></div></div>
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