<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 style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">
<DIV>I propose to amend my suggested "Unmanipulable Majority"</DIV>
<DIV>criterion by simply adding a phrase beginning with "without.." <BR>so that it now reads:</DIV>
<DIV> </DIV>
<DIV>*If (assuming there are more than two candidates) the ballot <BR>rules don't constrain voters to expressing fewer than three <BR>preference-levels, and A wins being voted above B on more <BR>than half the ballots, then it must not be possible to make B <BR>the winner by altering any of the ballots on which B is voted <BR>above A without raising their ranking or rating of B.*</DIV>
<DIV> </DIV>
<DIV>(Later I might rephrase it just to make it more succinct and</DIV>
<DIV>polished).</DIV>
<DIV><BR>The effect of the alteration is to preclude Compromise strategy.</DIV>
<DIV>When I first suggested the original version I knew that many methods</DIV>
<DIV>fail it due to Burial and/or Push-over, but I mistakenly thought that</DIV>
<DIV>my recent 3-slot method suggestion (defined below) meets it.<BR></DIV>
<DIV><BR>*Voters fill out 3-slot ratings ballots, default rating is bottom-most<BR>(indicating least preferred and not approved).<BR><BR>Interpreting top and middle rating as approval, disqualify all candidates<BR>with an approval score lower than their maximum approval-opposition (MAO) </DIV>
<DIV>score.<BR>(X's MAO score is the approval score of the most approved candidate on<BR>ballots that don't approve X).<BR><BR>Elect the undisqualified candidate with the highest top-ratings score.*</DIV>
<DIV> </DIV>
<DIV>My preferred name for that method is now "Strong Minimal Defense, Top</DIV>
<DIV>Ratings" (SMD,TR). <BR><BR>45: A<BR>03: A>B<BR>47: B>A</DIV>
<DIV>02: X>B</DIV>
<DIV>03: Y>A<BR><BR>Approvals: A98, B52, Y3, X2<BR>Max. AO: A2, B48, Y95, X95</DIV>
<DIV>Top Ratings: A48, B47, Y3, X2.</DIV>
<DIV><BR>X and Y are disqualified, and A wins.</DIV>
<DIV> </DIV>
<DIV>A is voted above B on more than half the ballots, but if all the ballots on<BR>which B is voted above A are altered so that they all plump for B (top-rate B</DIV>
<DIV>and approve no other candidates) then B wins.<BR><BR><BR>45: A<BR>03: A>B<BR>49: B
<DIV>03: Y>A<BR><BR>Approvals: A51, B52, Y3, X0<BR>Max. AO: A49, B48, Y52, X52</DIV>
<DIV>Top Ratings: A48, B49, Y3, X0<BR><BR>As before only X and Y are disqualified, but now B has the highest Top Ratings</DIV>
<DIV>score.</DIV>
<DIV> </DIV>
<DIV>I will soon post more on the subject of which methods meet or fail the (newly</DIV>
<DIV>amended) Unmanipulable Majority criterion.<BR></DIV>
<DIV>Chris Benham</DIV></DIV>
<DIV> </DIV>
<DIV><BR> </DIV>
<DIV> </DIV>
<DIV><BR><BR> </DIV></DIV></div><br>
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