<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px"><div><span>Hi Toby,</span></div><div style="color: rgb(0, 0, 0); font-size: 12px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-style: normal; background-color: transparent;"><span><br></span></div><div style="color: rgb(0, 0, 0); font-size: 12px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-style: normal; background-color: transparent;"><span>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 style="color: rgb(0, 0, 0); font-size: 12px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-style: normal; background-color:
transparent;"><span><br></span></div><div style="color: rgb(0, 0, 0); font-size: 12px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-style: normal; background-color: transparent;"><span>River's "ranking" can fail to order two candidates, despite there being a pairwise winner between them.</span></div><div style="color: rgb(0, 0, 0); font-size: 12px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-style: normal; background-color: transparent;"><span><br></span></div><div style="color: rgb(0, 0, 0); font-size: 12px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-style: normal; background-color: transparent;"><span>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 style="color: rgb(0, 0, 0); font-size: 12px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-style: normal; background-color: transparent;"><span><br></span></div><div style="color: rgb(0, 0, 0); font-size: 12px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-style: normal; background-color: transparent;"><span>Kevin Venzke</span></div><div><br></div> <div style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 12px;"> <div style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 16px;"> <div dir="ltr"> <hr size="1"> <font size="2" face="Arial">
<b><span style="font-weight:bold;">De :</span></b> Toby Pereira <tdp201b@yahoo.co.uk><br> <b><span style="font-weight: bold;">À :</span></b> "election-methods@electorama.com" <election-methods@electorama.com> <br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Lundi 3 novembre 2014 19h00<br> <b><span style="font-weight: bold;">Objet :</span></b> [EM] Condorcet methods - should the cycle order always determine the result order?<br> </font> </div> <div class="y_msg_container"><br><div id="yiv5420934475"><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>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><br></div><div>11: A>B>C</div><div>10: B>C>A</div><div>10: C>A>B</div><div>8: A>C>B</div><div><br></div><div>A beats B 29:10</div><div>C beats A 20:19</div><div>B beats C
21:18</div><div><br></div><div>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></div><div>1. There is a reasonable Condorcet method that would rank them A>C>B</div><div>2. The intuition that C should finish ahead of B is poorly thought out.</div><div>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>4. Other?</div></div></div></div><br><br></div> </div> </div> </div></body></html>