<html><head><style type="text/css"><!-- DIV {margin:0px;} --></style></head><body><div style="font-family:times new roman, new york, times, serif;font-size:12pt"><DIV>I have an idea for a new 3-slot voting method:</DIV>
<DIV> </DIV>
<DIV>*Voters fill out 3-slot ratings ballots, default rating is bottom-most</DIV>
<DIV>(indicating least preferred and not approved).</DIV>
<DIV><BR>Interpreting top and middle rating as approval, disqualify all candidates</DIV>
<DIV>with an approval score lower than their approval-opposition (AO) score.</DIV>
<DIV>(X's AO score is the approval score of the most approved candidate on</DIV>
<DIV>ballots that don't approve X).<BR></DIV>
<DIV>Elect the undisqualified candidate with the highest top-ratings score.*</DIV>
<DIV> </DIV>
<DIV>This clearly meets Favourite Betrayal, Participation, mono-raise, mono-append,</DIV>
<DIV>3-slot Majority for Solid Coalitions, "Strong Minimal Denfense" (and so Minimal</DIV>
<DIV>Defense and Woodall's Plurality criterion), Independence of Irrelevant Ballots.<BR></DIV>
<DIV>This "3-slot Strong Minimal Defense, Equal-Ranking First-Preference Plurality </DIV>
<DIV>(Whole)" method is my new clear favourite 3-slot single-winner method.</DIV>
<DIV> </DIV>
<DIV>One small technical disadvantage it has compared to Majority Choice Approval (MCA)</DIV>
<DIV>and ER-Bucklin(Whole) and maybe Kevin Venzke's ICA method is that it fails<BR>what I've been calling "Possible Approval Winner" (PAW).</DIV>
<DIV> </DIV>
<DIV>35: A<BR>10: A=B</DIV>
<DIV>30: B>C</DIV>
<DIV>25: C</DIV>
<DIV><BR>Approval scores: A45, B40, C55</DIV>
<DIV>Approval Opp.: A55, B35, C45<BR>Top-ratings score: A45, B40, C25. </DIV>
<DIV> </DIV>
<DIV>C's approval opposition to A is 55, higher than A's approval score of 45, so A is</DIV>
<DIV>disqualified. The undisqualified candidate with the highest top-ratings score is B,</DIV>
<DIV>so B wins. But if we pretend that on each ballot there is an invisible approval</DIV>
<DIV>threshold that makes some distinction among the candidates but not among those<BR>with the same rank, then B cannot have an approval score as high a A's.</DIV>
<DIV> </DIV>
<DIV>This example is from Kevin Venzke, which he gave to show that Schulze (also) elects</DIV>
<DIV>B and so fails this criterion. It doesn't bother me very much. MCA and Bucklin elect<BR>C.<BR></DIV>
<DIV>It is more Condorcetish and has a less severe later-harm problem than MCA, Bucklin,</DIV>
<DIV>or Cardinal Ratings (aka Range, Average Rating, etc.)<BR></DIV>
<DIV>40: A>B<BR>35: B<BR>25: C<BR></DIV>
<DIV>Approval scores: A40, B75, C25
<DIV>Approval Opp.: A35, B25, C75<BR>Top-ratings scores: A40, B35, C25 </DIV><BR></DIV>
<DIV>They elect B, but SMD,FPP(w) elects the Condorcet winner A.</DIV>
<DIV> </DIV>
<DIV>It seems a bit less vulnerable to Burial strategy than Schulze.</DIV>
<DIV> </DIV>
<DIV>46: A>B<BR>44: B>C (sincere is B>A)</DIV>
<DIV>05: C>A<BR>05: C>B</DIV>
<DIV> </DIV>
<DIV>Approval scores: A51, B95, C54
<DIV>Approval Opp.: A49, B05, C46<BR>Top-ratings scores: A46, B44, C10. </DIV>
<DIV> </DIV>
<DIV>In this admittedly not very realistic scenario, no candidate is disqualified and so A</DIV>
<DIV>wins. Schulze elects the buriers' favourite B.<BR></DIV>
<DIV><BR>Chris Benham</DIV></DIV>
<DIV> </DIV>
<DIV><BR> </DIV>
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<DIV> </DIV></div><br>Send instant messages to your online friends http://au.messenger.yahoo.com </body></html>