<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"> "I also think that FBC and (voted ballot) Condorcet are not incompatible for a 3-slot ballot."</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Jameson,</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Thanks for sharing this (based-on-who-knows-what) thought. Your problem with Kevin Venzke's</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">June 2005 3-candidate demonstration that FBC and Condorcet are incompatible (pasted below)<BR>is....what?</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Chris Benham</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto"><A style="RIGHT: auto" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-June/016410.html">http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-June/016410.html</A></SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Hello,<BR><BR>This is an attempt to demonstrate that Condorcet and FBC are incompatible.<BR>I modified Woodall's proof that Condorcet and LNHarm are incompatible.<BR>(Douglas R. Woodall, "Monotonicity of single-seat preferential election rules",<BR>Discrete Applied Mathematics 77 (1997), pages 86 and 87.)<BR><BR>I've suggested before that in order to satisfy FBC, it must be the case<BR>that increasing the votes for A over B in the pairwise matrix can never <BR>increase the probability that the winner comes from {a,b}; that is, it must<BR>not move the win from some other candidate C to A. This is necessary because<BR>if sometimes it were possible to move the win from C to A by increasing<BR>v[a,b], the voter with the preference order B>A>C would have incentive to<BR>reverse B and A in his ranking (and equal ranking would be inadequate).<BR><BR>I won't presently try to argue that this requirement
can't be avoided somehow.<BR>I'm sure it can't be avoided when the method's result is determined solely<BR>from the pairwise matrix.<BR><BR>Suppose a method satisfies this property, and also Condorcet. Consider this <BR>scenario:<BR><BR>a=b 3<BR>a=c 3<BR>b=c 3<BR>a>c 2<BR>b>a 2<BR>c>b 2<BR><BR>There is an A>C>B>A cycle, and the scenario is "symmetrical," as based on<BR>the submitted rankings, the candidates can't be differentiated. This means<BR>that an anonymous and neutral method has to elect each candidate with 33.33%<BR>probability.<BR><BR>Now suppose the a=b voters change their vote to a>b (thereby increasing v[a,b]).<BR>This would turn A into the Condorcet winner, who would have to win with 100% <BR>probability due to Condorcet.<BR><BR>But the probability that the winner comes from {a,b} has increased from 66.67%<BR>to 100%, so the first property is violated.<BR><BR>Thus the first property and Condorcet are incompatible, and I
contend that FBC<BR>requires the first property.<BR><BR>Thoughts?<BR><BR>Kevin Venzke<BR><BR><BR></div>
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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> Chris Benham <cbenhamau@yahoo.com.au> <BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> "fsimmons@pcc.edu" <fsimmons@pcc.edu>; MIKE OSSIPOFF <nkklrp@hotmail.com>; em <election-methods@electorama.com> <BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Tuesday, 22 November 2011 8:30 PM<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [EM] An ABE solution<BR></FONT><BR>
<DIV style="RIGHT: auto" id=yiv1309419319>I agree it's silly to create complicated rules for a two-slot ballot. But, though Forest didn't quite say so, I also think that FBC and (voted ballot) Condorcet are not incompatible for a 3-slot ballot.
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<DIV style="RIGHT: auto">Jameson<BR><BR>
<DIV style="RIGHT: auto" class=yiv1309419319gmail_quote>2011/11/22 Chris 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><BR>
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<DIV><SPAN>Forest,</SPAN></DIV>
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<DIV><SPAN>"When the range ballots have only two slots, the method is simply Approval, which does satisfy the <BR>FBC."</SPAN></DIV>
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<DIV><SPAN>When you introduced the method you suggested that 3-slot ballots be used "for simplicity".<BR>I thought you might be open to say 4-6 slots, but a complicated algorithm on 2-slot ballots</SPAN></DIV>
<DIV><SPAN>that is equivalent to Approval ??</SPAN></DIV>
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<DIV><SPAN>"Now consider the case of range ballots with three slots: and suppose that optimal strategy requires the <BR>voters to avoid the middle slot. Then the method reduces to Approval, which does satisfy the FBC."</SPAN></DIV>
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<DIV><SPAN>The FBC doesn't stipulate that all the voters use "optimal strategy", so that isn't relavent.<BR></SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto"><BR><VAR id=yui-ie-cursor></VAR><A style="RIGHT: auto" href="http://wiki.electorama.com/wiki/FBC" rel=nofollow target=_blank>http://wiki.electorama.com/wiki/FBC</A></SPAN></DIV>
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<DIV><SPAN><A href="http://nodesiege.tripod.com/elections/#critfbc" rel=nofollow target=_blank>http://nodesiege.tripod.com/elections/#critfbc</A><BR><BR>Chris Benham<VAR></VAR></SPAN></DIV>
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