<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div style="RIGHT: auto"><SPAN style="RIGHT: auto">Jameson,</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">You're not missing anything. You are right. Thanks for pointing that out.<BR></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">I should have thought more about those methods before suggesting them. </SPAN><SPAN style="RIGHT: auto">I withdraw those suggestions.</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">I still stand by APPMM as a good criterion. But the set can't be a component of a method algorithm that</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">meets the FBC.</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Chris Benham<VAR id=yui-ie-cursor></VAR></div></SPAN>
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<DIV style="BORDER-BOTTOM: #ccc 1px solid; BORDER-LEFT: #ccc 1px solid; PADDING-BOTTOM: 0px; LINE-HEIGHT: 0; MARGIN: 5px 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; HEIGHT: 0px; FONT-SIZE: 0px; BORDER-TOP: #ccc 1px solid; BORDER-RIGHT: #ccc 1px solid; PADDING-TOP: 0px" class=hr contentEditable=false readonly="true"></DIV><B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Jameson Quinn <jameson.quinn@gmail.com><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> C.Benham <cbenhamau@yahoo.com.au> <BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> em <election-methods@electorama.com> <BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Wednesday, 25 January 2012 5:11 AM<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [EM] Two more 3-slot FBC/ABE solutions<BR></FONT></DIV><BR>
<DIV id=yiv649437089>In fact, that would seem to be a pretty strong argument that these methods don't meet the FBC. What am I missing?<BR><BR>
<DIV class=yiv649437089gmail_quote>2012/1/24 Jameson Quinn <SPAN dir=ltr><<A href="mailto:jameson.quinn@gmail.com" rel=nofollow target=_blank ymailto="mailto:jameson.quinn@gmail.com">jameson.quinn@gmail.com</A>></SPAN><BR>
<BLOCKQUOTE style="BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex; PADDING-LEFT: 1ex" class=yiv649437089gmail_quote>The problem with these methods is that you can't afford to vote for the marginal candidate whom only you have heard of, because that candidate will not be part of any S, and so your ballot will count against any S, even an S that you otherwise like.<BR><BR>Jameson<BR><BR>
<DIV class=yiv649437089gmail_quote>2012/1/24 C.Benham <SPAN dir=ltr><<A href="mailto:cbenhamau@yahoo.com.au" rel=nofollow target=_blank ymailto="mailto:cbenhamau@yahoo.com.au">cbenhamau@yahoo.com.au</A>></SPAN>
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<BLOCKQUOTE style="BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex; PADDING-LEFT: 1ex" class=yiv649437089gmail_quote>Following on from my recent definition of the APPMM criterion/set, I'd like to propose two not bad 3-slot methods that meet the FBC..<BR><BR>Recall that I defined the APPMM criterion thus:<BR><BR>
<BLOCKQUOTE style="BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex; PADDING-LEFT: 1ex" class=yiv649437089gmail_quote>*If the number of ballots on which some set S of candidates is voted strictly above all the candidates outside S is greater than the number of ballots on which any outside-S candidate is voted strictly above any member of S, then the winner must come from S.* <BR></BLOCKQUOTE><BR><BR>The APPMM set is the set of candidates not disqualified by the APPMM criterion.<BR><BR>APMM//TR:<BR><BR>* Voters fill out 3-slot ratings ballots. Default rating is Bottom (signifying least preferred and not approved.) The other slots are Top (signifying most preferred) and Middle.<BR><BR>From the set of candidates not disqualified by the APPMM criterion, elect the one with the most Top ratings.*<BR><BR><BR>APMM//CR:<BR><BR>* Voters fill out 3-slot ratings ballots. Default rating is Bottom (signifying least preferred and not approved.) The other slots
are Top (signifying most preferred) and Middle.<BR><BR>From the set of candidates not disqualified by the APPMM criterion, elect the one with the highest Top minus Bottom ratings score.*<BR><BR><BR>So far I can't see that these are technically any better than my earlier suggestion of TTPBA//TR, and unlike that method they fail the "Tied at the Top Pairwise Beats All" criterion.<BR><BR>But like that method they meet the Plurality and Mono-add-Plump criteria, and also have no problem with Kevin's bad MMPO example.<BR><BR>I'm happy for APMM//CR to be also called APMM//Range. This method is more Condorcetish than APMM//TR, for example:<BR><BR>49: C>B<BR>27: A>B<BR>24: B>A<BR><BR>B>A 73-27, B>C 51-49, A>C 51-49.<BR><BR>APMM//TR elects A, while APMM//CR elects B (like TTPBA//TR).<BR><BR>I am sure that APMM//TR has no defection incentive in the "Approval Bad Example", and the other method also does in
the example normally given.<BR><BR>Of course some other points-score scheme (perhaps giving greater weight to to Top Ratings) is possible.<BR><BR>Chris Benham<BR><BR><BR><BR><BR>----<BR>Election-Methods mailing list - see <A href="http://electorama.com/em" rel=nofollow target=_blank>http://electorama.com/em</A> for list info<BR></BLOCKQUOTE></DIV></DIV></DIV><BR></BLOCKQUOTE></DIV><BR></DIV><BR><BR></DIV></DIV></div></body></html>