<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">Forest,<BR style="RIGHT: auto"></SPAN><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">In reference to your new Condorcet method suggestion (pasted at the bottom), which elects an<BR>uncovered candidate and if there is none one-at-time disqualifies the Range loser until a remaining</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">candidate X covers all the other remaining candidates and then elects X, you wrote:<BR></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">"Indeed, the three slot case does appear to satisfy the FBC..".<BR><BR>No. Here is my example, based on that Kevin Venke proof you didn't like.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Say sincere is</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">3: B>A</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">3: A=C<BR>3: B=C</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">2: A>C<BR>2: B>A</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">2: C>B</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">1: C</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Range (0,1,2) scores: C19, B17, A12.<BR></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">C>B 8-5, B>A 10-5, A>C 7-6.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">C wins.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Now we focus on the 3 B>A preferrers. Suppose (believing the method meets the FBC)</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">they vote B=A.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"> </div></SPAN><SPAN style="RIGHT: auto">
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">3: B=A (sincere is B>A)</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">3: A=C<BR>3: B=C</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">2: A>C<BR>2: B>A</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">2: C>B</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">1: C</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div><SPAN style="RIGHT: auto">
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Range (0,1,2) scores: C19, B17, A15.<BR><BR></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">C>B 8-5, B>A 7-5, A>C 7-6.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">C still wins.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Now suppose they instead rate their sincere favourite Middle:</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"><SPAN style="RIGHT: auto"><SPAN style="RIGHT: auto">3: A>B (sincere is B>A)</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">3: A=C<BR>3: B=C</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">2: A>C<BR>2: B>A</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">2: C>B</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">1: C</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div><SPAN style="RIGHT: auto">
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Range (0,1,2) scores: C19, A15, B12.<BR><BR>A>B 8-7, A>C 7-6, C>B 8-5</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Now those 3 voters get a result they prefer, the election of their compromise</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">candidate A. Since it is clear they couldn't have got a result for themselves as</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">good or better by voting B>A or B>C or B this is a failure of the FBC.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"><VAR id=yui-ie-cursor></VAR>Chris Benham</div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div></SPAN></SPAN></SPAN></SPAN>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"></SPAN></SPAN><SPAN style="RIGHT: auto"> </div></SPAN></SPAN>
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<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" class=ms__id15886><B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> "fsimmons@pcc.edu" <fsimmons@pcc.edu><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Wednesday, 23 November 2011 9:01 AM<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: An ABE solution<BR></FONT><BR>You are right that although the method is defined for any number of slots, I suggested three slots as <BR>most practical.<BR><BR>So my example of two slots was only to disprove the statement the assertion that the method cannot be <BR>FBC compliant, since it is obviously compliant in that case. <BR><BR>Furthermore something must be wrong with the quoted proof (of the incompatibility of the FBC and the <BR>CC) because the winner of the two slot case can be found entirely on the basis of the pairwise matrix. <BR>The other escape hatch is to say that two slots are not
enough to satisfy anything but the voted ballots <BR>version of the Condorcet Criterion. But this applies equally well to the three slot case.<BR><BR>Either way the cited "therorem" is not good enough to rule out compliance with the FBC by this new <BR>method.<BR><BR>Indeed, the three slot case does appear to satisfy the FBC as well. It is an open question. I did not <BR>assert that it does. But I did say that "IF" it is strategically equivalent to Approval (as Range is, for <BR>example) then for "practical purposes" it satisfies the FBC. Perhaps not the letter of the law, but the <BR>spirit of the law. Indeed, in a non-stratetgical environment nobody worries about the FBC, i.e. only <BR>strategic voters will betray their favorite. If optimal strategy is approval strategy, and approval strategy <BR>requires you to top rate your favorite, then why would you do otherwise?<BR><BR>Forest<BR><BR>----- Original Message
-----<BR>From: Chris Benham <BR><BR> Forest,<BR> <BR> "When the range ballots have only two slots, the method is simply Approval, which does satisfy the <BR> FBC."<BR> <BR> 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<BR> that is equivalent to Approval ??<BR> <BR> "Now consider the case of range ballots with three slots: and suppose that optimal strategy requires the </DIV>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" class=ms__id15886>voters to avoid the middle slot. Then the method reduces to Approval, which does satisfy the FBC."<BR> <BR> The FBC doesn't stipulate that all the voters use "optimal strategy", so that isn't relavent.<BR> <BR> <A href="http://wiki.electorama.com/wiki/FBC" target=_blank>http://wiki.electorama.com/wiki/FBC</A><BR> <BR> <A href="http://nodesiege.tripod.com/elections/#critfbc" target=_blank>http://nodesiege.tripod.com/elections/#critfbc</A><BR> <BR> Chris Benham<BR></DIV>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" class=ms__id15886>Forest Simmons wrote (17 Nov 2011):</DIV>
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<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt" class=ms__id15886>Here’s my current favorite deterministic proposal: Ballots are Range Style, say three slot for simplicity.<BR><BR>When the ballots are collected, the pairwise win/loss/tie relations are<BR>determined among the candidates.<BR><BR>The covering relations are also determined. Candidate X covers candidate Y if X<BR>beats Y as well as every candidate that Y beats. In other words row X of the<BR>win/loss/tie matrix dominates row Y.<BR><BR>Then starting with the candidates with the lowest Range scores, they are<BR>disqualified one by one until one of the remaining candidates X covers any other<BR>candidates that might remain. Elect X.<BR><BR></DIV></DIV></div></body></html>