<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><BR>--- En date de : Dim 19.10.08, Chris Benham <<A href="http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com"><FONT color=#810081>cbenhamau at yahoo.com.au</FONT></A>> a écrit :<BR>><I> I have an idea for a new 3-slot voting method:<BR></I>><I> <BR></I>><I> *Voters fill out 3-slot ratings ballots, default rating is<BR></I>><I> bottom-most </I><I>(indicating least preferred and not approved).<BR></I>><I> <BR></I>><I> Interpreting top and middle rating as approval, disqualify<BR></I>><I> all candidates </I><I>with an approval score lower than their approval-opposition<BR></I>><I> (AO) score.<BR></I>><I> (X's AO score is the approval score of the most </I><I>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<BR></I>><I> top-ratings score.*</I></DIV>
<P><I> </P>
<DIV><BR></I>Kevin Venzke wrote (Mon.Oct.20):</DIV>
<DIV><BR>Interesting method, but I'm concerned that rating a candidate in the <BR>middle can disqualify other candidates, but can't help this candidate <BR>win, except by preventing him from being disqualified himself. It seems<BR>like a burial risk.<BR><BR>With two major factions supporting A and B, and a third candidate C,<BR>if A faction buries B under C, I believe A will often win. Does B faction<BR>have a defensive strategy that isn't the same as the offensive strategy?<BR>I don't think they do.<BR><BR>Actually, this method isn't that far from MDD,FPP.</DIV>
<DIV> </DIV>
<DIV>CB: Except that method fails Irrelevant Ballots and I think meets LNHarm.<BR><BR>><I> This clearly meets Favourite Betrayal, Participation,<BR></I>><I> mono-raise, mono-append,<BR></I>><I> 3-slot Majority for Solid Coalitions, "Strong Minimal<BR></I>><I> Denfense" (and so Minimal<BR></I>><I> Defense and Woodall's Plurality criterion),<BR></I>><I> Independence of Irrelevant Ballots.<BR></I><BR>I don't think it satisfies Participation, because your favorite candidate<BR>could be winning, and when your vote is added, you add sufficient<BR>approval to your compromise choice that they are no longer disqualified,<BR>and are able to win instead of your favorite.</DIV>
<DIV> </DIV>
<DIV>CB: Oops!.. you are right. It fails Participation and even Mono-add-Top.</DIV>
<DIV> </DIV>
<DIV>8: C</DIV>
<DIV>3: F<BR>2: X>F</DIV>
<DIV>2: Y>F</DIV>
<DIV>2: Z>F</DIV>
<DIV> </DIV>
<DIV>F wins after all other candidates are disqualified, but if 2 F>C ballots are</DIV>
<DIV>added C wins in exactly the way you describe.</DIV>
<DIV> </DIV>
<DIV>It looks like the "Strong Minimal Defense" mechanism is incompatible with<BR>Participation, so I was also wrong in suggesting that my recent "Range-Approval</DIV>
<DIV>hybrid" method suggestion meets Participation.</DIV>
<DIV> </DIV>
<DIV>I still like this 3-slot SMD,FPP(w) method however and am confident the other<BR>criterion compliances I claimed for it hold up.<BR></DIV>
<DIV> </DIV>
<DIV>Chris Benham</DIV>
<DIV><BR><BR> </DIV></div><br>Send instant messages to your online friends http://au.messenger.yahoo.com </body></html>