<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,</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">"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 style="RIGHT: auto"><SPAN style="RIGHT: auto">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 style="RIGHT: auto"><SPAN style="RIGHT: auto">that is equivalent to Approval ??</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">"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 style="RIGHT: auto"><SPAN style="RIGHT: auto">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"><A style="RIGHT: auto" href="http://wiki.electorama.com/wiki/FBC">http://wiki.electorama.com/wiki/FBC</A></SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto"><A style="RIGHT: auto" href="http://nodesiege.tripod.com/elections/#critfbc">http://nodesiege.tripod.com/elections/#critfbc</A><BR><BR>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> "fsimmons@pcc.edu" <fsimmons@pcc.edu><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>; MIKE OSSIPOFF <nkklrp@hotmail.com> <BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Tuesday, 22 November 2011 11:11 AM<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: An ABE solution<BR></FONT><BR><BR><BR>From: "C.Benham" <BR><BR>> <BR>> Forest Simmons, responding to questions from Mike Ossipff, wrote <BR>> (19 Nov
<BR>> 2011):<BR>> <BR>> > > 4. How does it do by FBC? And by the criteria that bother some<BR>> > > people here about MMPO (Kevin's MMPO bad-example) and MDDTR <BR>> > (Mono-Add-Plump)?<BR>> ><BR>> > I think it satisfies the FBC.<BR>> <BR>> Forest's definition of the method being asked about:<BR>> <BR>> > Here’s my current favorite deterministic proposal: Ballots are <BR>> Range <BR>> > Style, say three slot for simplicity.<BR>> ><BR>> > When the ballots are collected, the pairwise win/loss/tie <BR>> relations are<BR>> > determined among the candidates.<BR>> ><BR>> > The covering relations are also determined. Candidate X covers <BR>> > candidate Y if X<BR>> > beats Y as well as every candidate that Y beats. In other <BR>> words row X <BR>> > of the<BR>> > win/loss/tie matrix dominates row Y.<BR>> ><BR>> > Then
starting with the candidates with the lowest Range <BR>> scores, they are<BR>> > disqualified one by one until one of the remaining candidates <BR>> X covers <BR>> > any other<BR>> > candidates that might remain. Elect X.<BR>> <BR>> <BR>> Forest,<BR>> <BR>> Doesn't this method meet the Condorcet criterion? Compliance <BR>> with <BR>> Condorcet is incompatible with FBC, so<BR>> why do you think it satisfies FBC?<BR><BR>When the range ballots have only two slots, the method is simply Approval, which does satisfy the <BR>FBC. Does Approval satisfy the Condorcet Criterion? I would say no, but it does satisfy the "votes only <BR>Condorcet Criterion." which means that the Approval winner X pairwise beats every other candidate Y <BR>according to the ballots, i.e. X is rated above Y on more ballots than Y is rated above X.<BR><BR>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.<BR><BR><BR>> <BR>> <BR>> <A href="http://lists.electorama.com/pipermail/election-methods-" target=_blank>http://lists.electorama.com/pipermail/election-methods-</A><BR>> electorama.com/2005-June/016410.html<BR>> <BR>> > Hello,<BR>> ><BR>> > This is an attempt to demonstrate that Condorcet and FBC are <BR>> incompatible.> I modified Woodall's proof that Condorcet and <BR>> LNHarm are incompatible.<BR>> > (Douglas R. Woodall, "Monotonicity of single-seat preferential <BR>> > 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 <BR>> the case<BR>> > that increasing the votes for A over B in the pairwise matrix <BR>> can never<BR>>
> increase the probability that the winner comes from {a,b}; <BR>> that is, it <BR>> > must<BR>> > not move the win from some other candidate C to A. This is <BR>> necessary <BR>> > because<BR>> > if sometimes it were possible to move the win from C to A by <BR>> increasing> v[a,b], the voter with the preference order B>A>C <BR>> would have incentive to<BR>> > reverse B and A in his ranking (and equal ranking would be <BR>> inadequate).><BR>> > I won't presently try to argue that this requirement can't be <BR>> avoided <BR>> > somehow.<BR>> > I'm sure it can't be avoided when the method's result is <BR>> determined solely<BR>> > from the pairwise matrix.<BR><BR>Note that in our method the Cardinal Ratings order (i.e. Range Order) is needed in addition to the <BR>pairwise matrix; the covering information comes from the pairwise matrix, but candidates are dropped
<BR>from the bottom of the range order.<BR><BR>In the two slot case can the approval order be determined from the pairwise matrix? If so, then this is a <BR>counterexample to the last quoted sentence above in the attempted proof of the incompatibility of the CC <BR>and the FBC.<BR><BR>Forest<BR><BR><BR></DIV></DIV></div></body></html>