<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_1_1445011240350_9634"><span>Hi Andy,</span></div><div id="yui_3_16_0_1_1445011240350_9633"><span><br></span></div><div id="yui_3_16_0_1_1445011240350_9633" dir="ltr"><span>If I take this example, looking at only 51 out of 100 voters (imagine the other 49 vote for other candidates entirely):</span></div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9627" class="">10 A>B</div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9627" class="">41 B>A</div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class=""><br id="yui_3_16_0_1_1445011240350_9821" class=""></div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class="">Under the original rule, all A voters will approve B, and 10 B voters will approve A. B probably wins. That seems fair. The B voters get an advantage from having more plurality votes.</div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class=""><br></div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class="">Under alternative 1, the smaller fraction is 100%. That would cause the two candidates to be tied at 51. (Or nearly tied, with a stray approval somewhere making the difference.) I think alternative 2 also gives this outcome. This seems a lot worse to me, because there's not really a sense that approvals constitute "lower" preferences.</div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class=""><br></div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class="">From the perspective of a sincere voter, the "approval" option signifies conditioning their opinion of a candidate on how that candidate's supporters vote. It's not such a crazy idea if one doesn't know much about a given candidate. I wonder if more can be done with the concept.</div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class=""><br></div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class="">My main concern with this type of method is the situation that a bloc of voters (supporting candidate A let's say) "defects" because they don't actually like candidate B. Even if B supporters know this is the situation, and even if B supporters would be willing to support A anyway, they don't have a (sincere) way of doing this.</div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class=""><br></div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class="">Kevin</div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class=""><br></div><div dir="ltr" id="yui_3_16_0_1_1445011240350_9819" class=""><br></div> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12px;" id="yui_3_16_0_1_1445011240350_9475"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_1_1445011240350_9474"> <div dir="ltr" id="yui_3_16_0_1_1445011240350_9473"> <hr size="1" id="yui_3_16_0_1_1445011240350_9939"> <font size="2" face="Arial"> <b><span style="font-weight:bold;">De :</span></b> Andy Jennings <elections@jenningsstory.com><br> <b><span style="font-weight: bold;">À :</span></b> Election Methods <election-methods@electorama.com> <br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Vendredi 16 octobre 2015 13h28<br> <b><span style="font-weight: bold;">Objet :</span></b> [EM] Cooperative voting<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_1_1445011240350_9777"><br><div id="yiv5323023503"><div dir="ltr" id="yui_3_16_0_1_1445011240350_9778">Cooperative voting<br>------------------<br>Voters indicate one favorite candidate and separately indicate all other candidates they approve of.<br><br>Approvals are an agreement to "conditionally cooperate". If A is my favorite but I also approved B, the approval for B will not count unless there is a corresponding B-voter who approved A.<br><br>Counting<br>--------<br>1. Candidates start with their plurality totals.<br><br>2. Each pair of candidates (A,B) is examined. Take the smaller of the number of A-voters who approved B and the number of B-voters who approved A and add it to both A's and B's totals.<br><br>Motivation<br>----------<br>Having run the straw poll for the Repulican Liberty Caucus last weekend, I've been thinking about approval voting, the chicken (Burr) dilemma, and the prisoners' dilemma.<br><br>One solution to a prisoners' dilemma situation is to offer "conditional cooperation".<br><br>Alternatives<br>------------<br>1) Use percentages instead. In step 2, let p equal the smaller of the fraction of A-voters who approved B and the fraction of B-voters who approved A. p times the number of A-voters is added to B's total. p times the number of B-voters is added to A's total.<br><br>2) Use non-approval instead. In step 2, let x equal the larger of the number of A-voters who did NOT approve B and the number of B-voters who did NOT approve A. The number of A-voters minus x (if positive) is added to B's total. The number of B-voters minus x (if positive) is added to A's total.<br><br>Questions<br>---------<br>Has this system been proposed before by another name?<br><br>How can it be abused?<br></div></div><br>----<br>Election-Methods mailing list - see <a href="http://electorama.com/em" target="_blank">http://electorama.com/em </a>for list info<br><br><br></div> </div> </div> </div></body></html>