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<div>Yes, this approach nicely follows the original idea of the method. Just make small random differences if there are none.</div><div><br class="webkit-block-placeholder"></div><div>Juho</div><div><br class="webkit-block-placeholder"></div><br><div><div>On Jan 1, 2008, at 19:43 , Diego Santos wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">2008/1/1, Steve Eppley <<a href="mailto:SEppley@alumni.caltech.edu">SEppley@alumni.caltech.edu</a>>:<div><span class="gmail_quote"></span><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> I think the method Diego Santos is considering can elect outside the<br>Smith set (a.k.a. top cycle), depending on the tie-breaker. Here's an<br>example with 21 voters and 4 candidates:<br><br> 4 4 4 3 3 3 <br> --- --- --- --- --- ---<br> A B C D D D<br> B C A A B C<br> C A B B C A<br> D D D C A B<br><br>{A,B,C} is a set of clones in a "vicious" cycle. (By vicious, I mean all <br>margins in the cycle are large. I think Mike Ossipoff may have been<br>first to use the term, many years ago.) What makes this scenario very<br>rare (assuming many voters) is that the margins in the vicious cycle are <br>equal:<br><br> A over B by (4+4+3+3) - (4+3) = 7<br> B over C by (4+4+3+3) - (4+3) = 7<br> C over A by (4+4+3+3) - (4+3) = 7<br><br>The Smith set is {A,B,C}. Can D win? If I understand Diego's<br>definition, D is not eliminated since the margin in D's pairwise defeats <br>is smallest (12 - 9 = 3). I think A and B and C are also not eliminated<br>since there's a tie in their cycle's margins. Thus the set of<br>non-eliminated candidates is {A,B,C,D}. Among {A,B,C,D} there is no <br>Condorcet winner. So, a tiebreaker must select from {A,B,C,D}. If the<br>tiebreaker can select outside the Smith set, D can be elected. Typical<br>tiebreakers (Random, Random Voter's Ballot, Chairperson's Choice) can <br>select outside the Smith set.<br><br></blockquote></div><br>A possible tiebraker can be: "if no Condorcet Winner exists among non-eliminated candidates, reuse this method with one of equal margins 'pseudo-augmented'" selected at random. <br><br>In Steve's example, we can select, for instance, B win over C as "pseudo-augmented" (marked with an asterisk):<br><br><span style="font-family: courier new,monospace;">A(7): C(7,7*)</span><br style="font-family: courier new,monospace;"> <span style="font-family: courier new,monospace;">B(7): A(7,7)</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;">C(7*): B(7*,7) eliminated</span><br style="font-family: courier new,monospace;"> <span style="font-family: courier new,monospace;">D(3): A(3,7), B(3,7), C(3,7*)<br><br></span>Then a member of the "vicious circle" is disqualified.<br><br>New set: {A, B, D}, and A wins. But uses of this tiebraker would be too rare. <br>________________________________<br>Diego Renato dos Santos<br><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">----</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Election-Methods mailing list - see <a href="http://electorama.com/em">http://electorama.com/em</a> for list info</div> </blockquote></div><br></body></html>