<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"><BR class=yui-cursor></SPAN></div>
<div style="RIGHT: auto">Jameson,</div>
<div style="RIGHT: auto"> </div>
<div style="RIGHT: auto">"Your range scores are a little bit wrong,.."<BR></div>
<div style="RIGHT: auto">I've re-checked them and I don't see how. I gave each candidate 2 points for a top-rating, 1 for a middle-rating</div>
<div style="RIGHT: auto">and zero for a bottom rating (or truncation).</div>
<div style="RIGHT: auto"> </div>
<div style="RIGHT: auto">So in the initial "sincere" scenario for example C has 9 top-ratings and 1 middle-rating to make a score of 19,</div>
<div style="RIGHT: auto">B has 8 top-ratings and 1 middle-rating to make a score of 17, and A has 5 top-ratings and 2 middle-ratings</div>
<div style="RIGHT: auto">to make a score of 12.</div>
<div style="RIGHT: auto"><BR style="RIGHT: auto">Chris Benham<VAR id=yui-ie-cursor></VAR></div>
<div style="RIGHT: auto"> </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">Sent:</SPAN></B> Friday, 25 November 2011 5:39 AM<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: An ABE solution<BR></FONT><BR>
<DIV style="RIGHT: auto" id=yiv313925662>Chris:
<DIV><BR></DIV>
<DIV style="RIGHT: auto">Your range scores are a little bit wrong, so you have to add half a B vote for the example to work (or double all factions and add one B vote if you discriminate against fractional people), but yes, this is at heart a valid example where the method fails FBC. </DIV>
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<DIV style="RIGHT: auto">Note that in my tendentious terminology this is only a "defensive" failure, that is, it starts from a position of a sincere condorcet cycle, which I believe will be rare enough in real elections to be discountable. In particular, this failure does not result in a stable two-party-lesser-evil-strategy self-reinforcing equilibrium.
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<DIV style="RIGHT: auto">Jameson<BR><BR>
<DIV style="RIGHT: auto" class=yiv313925662gmail_quote>2011/11/24 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,<BR></SPAN><SPAN></SPAN></DIV>
<DIV><SPAN>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><SPAN>candidate X covers all the other remaining candidates and then elects X, you wrote:<BR></SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN>"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><SPAN></SPAN> </DIV>
<DIV><SPAN>Say sincere is</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>3: B>A</SPAN></DIV>
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<DIV><SPAN>3: A=C<BR>3: B=C</SPAN></DIV>
<DIV><SPAN>2: A>C<BR>2: B>A</SPAN></DIV>
<DIV><SPAN>2: C>B</SPAN></DIV></DIV>
<DIV><SPAN>1: C</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>Range (0,1,2) scores: C19, B17, A12.<BR></SPAN></DIV>
<DIV><SPAN>C>B 8-5, B>A 10-5, A>C 7-6.</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>C wins.</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>Now we focus on the 3 B>A preferrers. Suppose (believing the method meets the FBC)</SPAN></DIV>
<DIV><SPAN>they vote B=A.</SPAN></DIV>
<DIV><SPAN> </SPAN></DIV><SPAN style="RIGHT: auto">
<DIV><SPAN>3: B=A (sincere is B>A)</SPAN></DIV>
<DIV style="RIGHT: auto" class=yiv313925662im>
<DIV style="RIGHT: auto"><SPAN>3: A=C<BR>3: B=C</SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN>2: A>C<BR>2: B>A</SPAN></DIV>
<DIV><SPAN>2: C>B</SPAN></DIV></DIV>
<DIV><SPAN>1: C</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV><SPAN style="RIGHT: auto">
<DIV><SPAN>Range (0,1,2) scores: C19, B17, A15.<BR><BR></SPAN></DIV>
<DIV><SPAN>C>B 8-5, B>A 7-5, A>C 7-6.</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>C still wins.</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN>Now suppose they instead rate their sincere favourite Middle:</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN><SPAN><SPAN>3: A>B (sincere is B>A)</SPAN></SPAN></SPAN></DIV>
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<DIV style="RIGHT: auto"><SPAN>3: A=C<BR>3: B=C</SPAN></DIV>
<DIV><SPAN>2: A>C<BR>2: B>A</SPAN></DIV>
<DIV><SPAN>2: C>B</SPAN></DIV></DIV>
<DIV><SPAN>1: C</SPAN></DIV>
<DIV><SPAN></SPAN> </DIV><SPAN style="RIGHT: auto">
<DIV><SPAN>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><SPAN></SPAN> </DIV>
<DIV><SPAN>Now those 3 voters get a result they prefer, the election of their compromise</SPAN></DIV>
<DIV><SPAN>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=A or B or B>C or B=C this is a failure</SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">of the FBC.</SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </DIV>
<DIV><SPAN><VAR></VAR>Chris Benham</SPAN></DIV>
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<DIV><SPAN></SPAN> </DIV>
<DIV><SPAN> </SPAN></DIV>
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<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt"><B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> "<A href="mailto:fsimmons@pcc.edu" rel=nofollow target=_blank ymailto="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</A>" <<A href="mailto:fsimmons@pcc.edu" rel=nofollow target=_blank ymailto="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</A>><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Wednesday, 23 November 2011 9:01 AM
<DIV class=yiv313925662im><BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: An ABE solution<BR></DIV></DIV></FONT>
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<DIV class=yiv313925662h5><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></DIV>
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<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt">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" rel=nofollow target=_blank>http://wiki.electorama.com/wiki/FBC</A><BR> <BR><A href="http://nodesiege.tripod.com/elections/#critfbc" rel=nofollow target=_blank>http://nodesiege.tripod.com/elections/#critfbc</A><BR> <BR>Chris Benham<BR></DIV></DIV></DIV>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt">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">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></DIV></BLOCKQUOTE></DIV><BR></DIV></DIV></DIV><BR><BR></DIV></DIV></div></body></html>