<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:13px"><div id="yiv0557005502"><div><div style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px; background-color: rgb(255, 255, 255);"><div id="yiv0557005502yui_3_16_0_6_1415113179090_4"><span id="yiv0557005502yui_3_16_0_6_1415113179090_13">Thank you Juho and Kevin for your replies. I agree with you both that the main point of a Condorcet method is to find a winner. Anything else is relatively unimportant. If, for example, we chose the Minimax method because we decided that it gave a better overall order, we might find cases where we'd disagree with the winner. So using something like Schulze or Ranked Pairs would still be better if we thought they were better at finding a winner regardless of what they said about the other
candidates.</span></div><div id="yiv0557005502yui_3_16_0_6_1415113179090_18" style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px; font-style: normal; background-color: transparent;"><span id="yiv0557005502yui_3_16_0_6_1415113179090_17"><br clear="none"></span></div><div id="yiv0557005502yui_3_16_0_6_1415113179090_20" style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px; font-style: normal; background-color: transparent;"><span id="yiv0557005502yui_3_16_0_6_1415113179090_19">With Schulze, I thought its beatpath method was transitive. I wasn't thinking of removing the winner and recalculating. Maybe I'm wrong about that. But yes, River obviously only affirms the pairwise results that it needs to in order to get a winner, so certainly can't be said to produce an overall ranking in all
cases.</span></div><div class="ms__id6568" style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px; font-style: normal; background-color: transparent;"><span><br></span></div><div class="ms__id6568" style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>But I was thinking that maybe a Condorcet method might be used to generate an ordering in a sporting competition, where you have head-to-head matches, and where you want to find more than just first place. I'm not sure many sports would want the added complication of Condorcet though.</span></div><div class="ms__id6568" style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px; font-style: normal; background-color:
transparent;"><span><br></span></div><div class="ms__id6568" style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>Toby</span></div><div id="yiv0557005502yui_3_16_0_6_1415113179090_15" style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px; font-style: normal; background-color: transparent;"><span id="yiv0557005502yui_3_16_0_6_1415113179090_14"><br clear="none"></span></div><div id="yiv0557005502yui_3_16_0_6_1415113179090_10"><br id="yiv0557005502yui_3_16_0_6_1415113179090_5" clear="none"><blockquote id="yiv0557005502yui_3_16_0_6_1415113179090_7" style="padding-left: 5px; margin-top: 5px; margin-left: 5px; border-left-color: rgb(16, 16, 255); border-left-width: 2px; border-left-style: solid;"> <div class="yiv0557005502ms__id4277"
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<b><span style="font-weight: bold;">From:</span></b> Kevin Venzke <stepjak@yahoo.fr><br clear="none"> <b><span style="font-weight: bold;">To:</span></b> em <election-methods@electorama.com> <br clear="none"> <b><span style="font-weight: bold;">Sent:</span></b> Tuesday, 4 November 2014, 13:47<br clear="none"> <b><span style="font-weight: bold;">Subject:</span></b> Re: [EM] Condorcet methods - should the cycle order always determine the result order?<br clear="none"> </font> </div> <div class="yiv0557005502y_msg_container" id="yiv0557005502yui_3_16_0_1_1415113179090_9550"><br clear="none"><div id="yiv0557005502"><div id="yiv0557005502yui_3_16_0_1_1415113179090_9549"><div class="yiv0557005502ms__id4284" id="yiv0557005502yui_3_16_0_1_1415113179090_9548" style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12px; background-color: rgb(255, 255, 255);"><div
id="yiv0557005502yui_3_16_0_1_1415113179090_9662"><span>Hi Toby,</span></div><div class="yiv0557005502ms__id4285" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><span><br clear="none"></span></div><div class="yiv0557005502ms__id4286" id="yiv0557005502yui_3_16_0_1_1415113179090_9547" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><span id="yiv0557005502yui_3_16_0_1_1415113179090_9546">Especially with more than three candidates I think it is unclear how to define second or third place under Schulze. Are you removing the winner and recalculating?</span></div><div class="yiv0557005502ms__id4287" id="yiv0557005502yui_3_16_0_1_1415113179090_9551" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><span><br clear="none"></span></div><div class="yiv0557005502ms__id4288" id="yiv0557005502yui_3_16_0_1_1415113179090_9553" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><span
id="yiv0557005502yui_3_16_0_1_1415113179090_9552">River's "ranking" can fail to order two candidates, despite there being a pairwise winner between them.</span></div><div class="yiv0557005502ms__id4289" id="yiv0557005502yui_3_16_0_1_1415113179090_9554" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><span><br clear="none"></span></div><div class="yiv0557005502ms__id4290" id="yiv0557005502yui_3_16_0_1_1415113179090_9556" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><span id="yiv0557005502yui_3_16_0_1_1415113179090_9555">I would say the only reason Ranked Pairs appears to indicate a ranking is that the only way we know how to find the RP winner is to construct this ranking. In other words, if you somehow find
another method of calculating the RP winner, which doesn't involve constructing the full ranking, then it would be unclear to me that RP says anything about second or third place.</span></div><div class="yiv0557005502ms__id4291" id="yiv0557005502yui_3_16_0_1_1415113179090_9640" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><span><br clear="none"></span></div><div class="yiv0557005502ms__id4292" id="yiv0557005502yui_3_16_0_1_1415113179090_9641" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><span>Kevin Venzke</span></div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9663"><br clear="none"></div> <div class="yiv0557005502ms__id4293" id="yiv0557005502yui_3_16_0_1_1415113179090_9647" style="font-family: HelveticaNeue,;"> <div class="yiv0557005502ms__id4294" id="yiv0557005502yui_3_16_0_1_1415113179090_9646" style="font-family: HelveticaNeue,;"> <div id="yiv0557005502yui_3_16_0_1_1415113179090_9661" dir="ltr"> <div
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<b><span style="font-weight: bold;">De :</span></b> Toby Pereira <tdp201b@yahoo.co.uk><br clear="none"> <b><span style="font-weight: bold;">À :</span></b> "election-methods@electorama.com" <election-methods@electorama.com> <br clear="none"> <b><span style="font-weight: bold;">Envoyé le :</span></b> Lundi 3 novembre 2014 19h00<br clear="none"> <b><span style="font-weight: bold;">Objet :</span></b> [EM] Condorcet methods - should the cycle order always determine the result order?<br clear="none"> </font> </div> <div class="yiv0557005502yqt9472810128" id="yiv0557005502yqt86000"><div class="yiv0557005502y_msg_container" id="yiv0557005502yui_3_16_0_1_1415113179090_9645"><br clear="none"><div id="yiv0557005502"><div id="yiv0557005502yui_3_16_0_1_1415113179090_9644"><div class="yiv0557005502ms__id4300" id="yiv0557005502yui_3_16_0_1_1415113179090_9643" style="color: rgb(0, 0, 0); font-family: HelveticaNeue,;"><div
id="yiv0557005502yui_3_16_0_1_1415113179090_9664">In a lot of the more preferred Condorcet methods (e.g. I think all of Schulze, Ranked Pairs, River, Kemeny), if you have, for example, an A>B>C>A cycle, then if, say, A wins then B will automatically finish second
and C third (if B wins, C will be second etc.). But you could have a similar number of A>B>C, B>C>A and C>A>B ballots but then also a lot of A>C>B ballots, meaning that in some sense C looks better than B. But as long as this doesn't break the cycle and A wins, then B will still finish second. I think the following example does it:</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9665"><br clear="none"></div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9642">11: A>B>C</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9658">10: B>C>A</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9657">10: C>A>B</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9656">8: A>C>B</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9659"><br clear="none"></div><div>A beats B 29:10</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9655">C beats A 20:19</div><div
id="yiv0557005502yui_3_16_0_1_1415113179090_9654">B beats C
21:18</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9653"><br clear="none"></div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9652">I'm not saying these methods are wrong for doing this, but there is an intuitive sense in which C is arguably a better choice than B. So is it:</div><div><br clear="none"></div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9651">1. There is a reasonable Condorcet method that would rank them A>C>B</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9650">2. The intuition that C should finish ahead of B is poorly thought out.</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9648">3. It is in a sense reasonable to think that C should finish ahead of B, but doing so would cause a method to fail certain criteria and end up worse as a result.</div><div id="yiv0557005502yui_3_16_0_1_1415113179090_9649">4. Other?</div></div></div></div><br clear="none"><br clear="none"></div></div> </div> </div>
</div></div></div><br clear="none"><div class="yiv0557005502yqt9472810128" id="yiv0557005502yqt35357">----<br clear="none">Election-Methods mailing list - see <a href="http://electorama.com/em" target="_blank" rel="nofollow" shape="rect">http://electorama.com/em</a>for list info<br clear="none"></div><br clear="none"><br clear="none"></div></div> </div> </div> </blockquote><div></div> </div></div></div></div></div></body></html>