<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>Kristofer,<BR>You wrote addressing me:<BR>"You have some examples showing that RP/Schulze/"etc" fail the criterion."</DIV>
<DIV> </DIV>
<DIV>By my lazy "etc." I just meant 'and the other Condorcet methods that are </DIV>
<DIV>all equivalent to MinMax when there are just 3 candidates and Smith//Minmax</DIV>
<DIV>when there are not more than 3 candidates in the Smith set'.</DIV>
<DIV> </DIV>
<DIV>"Do they show that Condorcet and UM is incompatible? Or have they just <BR>been constructed on basis of some Condorcet methods, with differing <BR>methods for each?"</DIV>
<DIV> </DIV>
<DIV>My intention was to show that all the methods that take account of more than </DIV>
<DIV>one possible voter preference-level (i.e. not Approval or FPP) (and are <BR>well-known and/or advocated by anyone on EM) are vulnerable to UM except <BR>SMD,TP.</DIV>
<DIV><BR>"I think I remember that you said Condorcet implies some vulnerability to <BR>burial. Is that sufficient to make it fail UM?"</DIV>
<DIV> </DIV>
<DIV>Probably yes, but I haven't tried to prove as much. </DIV>
<DIV> </DIV>
<DIV>Returning to this demonstration:</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>93: A<BR>09: B>A<BR>78: B<BR>14: C>B<BR>02: C>A<BR>04: C<BR>200 ballots<BR><BR>B>A 101-95, B>C 87-20, A>C 102-20.<BR>All Condorcet methods, plus MDD,X and MAMPO and ICA elect B.<BR><BR>B has a majority-strength pairwise win against A, but say 82 of the 93A change to<BR>A>C thus:<BR><BR>82: A>C<BR>11: A<BR>09: B>A<BR>78: B<BR>14: C>B<BR>02: C>A<BR>04: C<BR><BR>B>A 101-95, C>B 102-87, A>C 102-20<BR>Approvals: A104, B101, C102<BR>TR scores: A93, B87, C 20<BR><BR>Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using <BR>WV or Margins elect A. So all those methods fail the UM criterion.</DIV>
<DIV> </DIV>
<DIV>Working in exactly the same way as ICA (because no ballots have voted more than one candidate</DIV>
<DIV>top), this also applies to Condorcet//Approval and Smith//Approval and Schwartz//Approval.</DIV>
<DIV>So those methods also fail UM.</DIV>
<DIV><BR>"I did a bit of calculation and it seems my FPC (first preference <BR>Copeland) variant elects B here, as should plain FPC. Since it's <BR>nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure <BR>whether that can be fixed at all."</DIV>
<DIV> </DIV>
<DIV>My impression is/was that in 3-candidates-in-a-cycle examples that method behaves just like IRV.<BR>The demonstration that I gave of IRV failing UM certainly also applies to it. </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>Chris Benham<BR><BR><BR><BR><STRONG>Kristofer Munsterhjelm</STRONG> wrote (Thurs.Dec.4):</DIV>
<DIV>Chris Benham wrote:<BR>><I> Regarding my proposed Unmanipulable Majority criterion:<BR></I>><I> <BR></I>><I> *If (assuming there are more than two candidates) the ballot<BR></I>><I> rules don't constrain voters to expressing fewer than three<BR></I>><I> preference-levels, and A wins being voted above B on more<BR></I>><I> than half the ballots, then it must not be possible to make B</DIV>
</I>><I> the winner by altering any of the ballots on which B is voted<BR></I>><I> above A without raising their ranking or rating of B.*<BR></I>><I> <BR></I>><I> To have any point a criterion must be met by some method.<BR></I>><I> <BR></I>><I> It is met by my recently proposed SMD,TR method, which I introduced<BR></I>><I> as "3-slot SMD,FPP(w)":<BR></I>><I> <BR></I>><I> *Voters fill out 3-slot ratings ballots, default rating is bottom-most<BR></I>><I> (indicating least preferred and not approved).<BR></I>><I> <BR></I>><I> Interpreting top and middle rating as approval, disqualify all candidates<BR></I>><I> with an approval score lower than their maximum approval-opposition<BR></I>><I> (MAO) score.<BR></I>><I> (X's MAO score is the approval score of the most approved candidate on<BR></I>><I> ballots that don't approve X).<BR></I>><I> <BR></I>><I> Elect the undisqualified candidate
with the highest top-ratings score.*<BR></I>><I> <BR></I>[snip examples of methods failing the criterion]<BR><BR>You have some examples showing that RP/Schulze/"etc" fail the criterion. <BR>Do they show that Condorcet and UM is incompatible? Or have they just <BR>been constructed on basis of some Condorcet methods, with differing <BR>methods for each?<BR><BR>I think I remember that you said Condorcet implies some vulnerability to <BR>burial. Is that sufficient to make it fail UM? I wouldn't be surprised <BR>if it is, seeing that you have examples for a very broad range of <BR>election methods.<BR><BR>><I> 93: A<BR></I>><I> 09: B>A<BR></I>><I> 78: B<BR></I>><I> 14: C>B<BR></I>><I> 02: C>A<BR></I>><I> 04: C<BR></I>><I> 200 ballots<BR></I>><I> <BR></I>><I> B>A 101-95, B>C 87-20, A>C 102-20.<BR></I>><I> All Condorcet methods, plus MDD,X and MAMPO and ICA elect
B.<BR></I>><I> <BR></I>><I> B has a majority-strength pairwise win against A, but say 82 of the 93A <BR></I>><I> change to<BR></I>><I> A>C thus:<BR></I>><I> <BR></I>><I> 82: A>C<BR></I>><I> 11: A<BR></I>><I> 09: B>A<BR></I>><I> 78: B<BR></I>><I> 14: C>B<BR></I>><I> 02: C>A<BR></I>><I> 04: C<BR></I>><I> <BR></I>><I> B>A 101-95, C>B 102-87, A>C 102-20<BR></I>><I> Approvals: A104, B101, C102<BR></I>><I> TR scores: A93, B87, C 20<BR></I>><I> <BR></I>><I> Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using<BR></I>><I> WV or Margins elect A. So all those methods fail the UM criterion.<BR></I><BR>I did a bit of calculation and it seems my FPC (first preference <BR>Copeland) variant elects B here, as should plain FPC. Since it's <BR>nonmonotonic, it's vulnerable to Pushover, though, and I'm
not sure <BR>whether that can be fixed at all.<BR><!--endarticle--><!--htdig_noindex--></div><br>
<hr size=1>
Start your day with Yahoo!7 and win a Sony Bravia TV. <a href="http://au.rd.yahoo.com/hppromo/mail/tagline2/*http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline" target=_blank>Enter now</a>.</body></html>