<html><head><meta http-equiv="Content-Type" content="text/html charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div>One more observation on clones. I think there is a major difference between methods that systematically favour or disfavour groupings with multiple candidates (e.g. Borda where nomination of two candidates instead of one typically changes the results dramatically) and methods that can break the clone criterion in some exceptional situations. For example minmax can handle clones perfectly well if we study only those cases that do not have any loops. If we assume that loops are rare, or that they are weak if they happen to exist, also then there are no significant risks (nor benefits) if some groupings do nominate multiple candidates. I guess it is quite correct to say that in typical elections (where large number of voters make independet decisions) Borda has practical problems with clones, while minmax doesn't (although both formally violate the EM clone criterion). That difference is important when one looks for practical election methods (i.e. not just study theoretical properties of different methos / compliance with various formal criteria).</div><div><br></div><div>Juho</div><div><br></div><br><div><div>On 05 Nov 2014, at 22:54, Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk">tdp201b@yahoo.co.uk</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="background-color: rgb(255, 255, 255); font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 13px;"><div><span>Kemeny certainly wouldn't be my preferred choice, partly because of its lack of clone independence, but I mentioned it because it seems to come up frequently enough.</span></div><div style="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 style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>I think I remember seeing before your "done right" post. I'll have to read it again, because I remember considering the possibility of a cloneproof Borda before and deciding that any attempt to cloneproof
it would leave it unrecognisable from Borda. For example, if you have the following ballots:</span></div><div style="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 style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>10: A>B>C>D>E</span></div><div style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>10: B>C>D>E>A</span></div><div style="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 style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>Using Borda philosophy, B is the best here, but from the perspective of A, BCDE form a clone group, so any cloneproof system would have to consider A equal to each other candidate.</span></div><div style="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 style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>I think cloneproof Condorcet systems wouldn't have a set order here. While they would rank B>C>D>E, there
would be no specific place for A to go. And I think this is why (as people have said), Condorcet methods don't necessarily have a complete fixed order. For example, even though B beats C and A is equal to C, it is not the case that B beats A.</span></div><div style="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 style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>But back to Borda - if the cloneproof version of Borda uses scores (as normal Borda does), then I can't see a set of scores that would make sense here. We can have scores so that B>C>D>E. But any score for A doesn't work. Because A has to be equal to all of them!</span></div><div style="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 style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 13px; font-style: normal; background-color: transparent;"><span>But this also makes me wonder generally - are there any sensible cloneproof ranked-ballot systems that aren't Condorcet methods? IRV is cloneproof, but is it sensible? Is there anything else?</span></div><div><br><blockquote 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 style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px;"> <div style="font-family: HelveticaNeue, Helvetica Neue,
Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div dir="ltr"> <div class="hr" style="margin: 5px 0px; padding: 0px; border: 1px solid rgb(204, 204, 204); border-image: none; height: 0px; line-height: 0; font-size: 0px;" contenteditable="false" readonly="true"></div> <font face="Arial" size="2"> <b><span style="font-weight: bold;">From:</span></b> Forest Simmons <<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a>><br> <b><span style="font-weight: bold;">To:</span></b> EM <<a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a>> <br> <b><span style="font-weight: bold;">Sent:</span></b> Tuesday, 4 November 2014, 22:46<br> <b><span style="font-weight: bold;">Subject:</span></b> [EM] Condorcet methods - should the cycle order always determine the result order? (Toby Pereira)<br> </font> </div> <div class="y_msg_container"><br><div id="yiv2102699210"><div dir="ltr"><div><div><div>Toby,<br><br>You mentioned Kemeny. The very purpose of Kemeny is to determine a "social order,"
namely the one that minimizes the average "distance" from that order to the ballot orders..<br><br></div>The trouble with Kemeny is that the choice of metric for the "distance:" is clone dependent: changing the size of a clone set changes the number of transpositions of order to move a candidate past that set. <br><br>However, if cardinal ratings (e.g. score ballots) are used, then clone independent metrics can be substituted for the Kemeny distance. I once posted a message to this list describing a clone free technique for converting a set of ordinal ballots into a set of ratings Then based on those ratings it was possible to define "Kemeny Done Right," Dodgson Done Right," and "Borda Done Right." Of these three "done right" methods, only the latter fails the Condorcet Criterion.<br></div><br></div>Forest<br><div><br><br><br><br><div><div class="yiv2102699210gmail_extra"><br><br></div></div></div></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> </blockquote><div></div> </div></div>----<br>Election-Methods mailing list - see <a href="http://electorama.com/em">http://electorama.com/em</a> for list info<br></blockquote></div><br></body></html>