<html><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_1428964266634_3104" dir="ltr">Hi Chris,</div><div id="yui_3_16_0_1_1428964266634_3104" dir="ltr"><br></div><div id="yui_3_16_0_1_1428964266634_3104" dir="ltr">"Non-cyclic pairwise loss" just means a loss that wouldn't create a cycle of locked wins (at the time in the process that you consider the loss). RP has this concept just like River does. What makes River seem similar to a Minmax method is that only one loss (the strongest non-cyclic one) will get counted for any particular candidate. Once you lock a win against somebody, you won't lock any more against them.</div><div id="yui_3_16_0_1_1428964266634_3104" dir="ltr"><br></div><div id="yui_3_16_0_1_1428964266634_3104" dir="ltr">I can't say I had thought of it that way before, though.</div><div id="yui_3_16_0_1_1428964266634_3104" dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1428964266634_3104" dir="ltr"><span>Kevin</span></div><br> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12px;" id="yui_3_16_0_1_1428964266634_3103"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_1_1428964266634_3102"> <div dir="ltr" id="yui_3_16_0_1_1428964266634_3101"> <hr size="1" id="yui_3_16_0_1_1428964266634_3307"> <font size="2" face="Arial" id="yui_3_16_0_1_1428964266634_3706"> <b><span style="font-weight:bold;">De :</span></b> C.Benham <cbenham@adam.com.au><br> <b><span style="font-weight: bold;">À :</span></b> "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Lundi 13 avril 2015 13h10<br> <b><span style="font-weight: bold;">Objet :</span></b> "non-cyclic" pairwise loss?<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_1_1428964266634_3707"><br><div id="yiv5696790889">
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The Electowiki page on Heitzig's River method includes:<br>
<br>
<blockquote type="cite" id="yui_3_16_0_1_1428964266634_3743">River can be interpreted as a <a rel="nofollow" title="Minmax" target="_blank" href="http://wiki.electorama.com/wiki/Minmax">Minmax</a>
method, Minmax(non-cyclic pairwise loss) or MMNCPL. It is similar
to Minmax(winning votes) except that River elects the candidate
whose greatest <i>non-cyclic</i> pairwise loss to another
candidate is least. As in <a rel="nofollow" title="Ranked Pairs" target="_blank" href="http://wiki.electorama.com/wiki/Ranked_Pairs">Ranked Pairs</a>,
the greatest pairwise loss (GPL) of each candidate is considered
in order from largest (among all candidates) to smallest and
locked. If a candidate's GPL is cyclic, it is discarded, and the
next-greatest pairwise loss of that candidate is added to the
list. When the non-cyclic greatest pairwise losses of (N-1)
candidates have been locked, the remaining candidate is the
winner. </blockquote>
<br>
<a rel="nofollow" class="yiv5696790889moz-txt-link-freetext" target="_blank" href="http://wiki.electorama.com/wiki/River">http://wiki.electorama.com/wiki/River</a><br>
<br>
What is the clear and simple definition of a "cyclic" pairwise
loss? <br>
<br>
If all the candidates are in the Smith set, aren't *all* the
pairwise losses (at least in some sense) "cyclic"?<br>
<br>
Chris Benham<br>
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