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.<div><br></div>
<div>Jameson<br><br><div class="gmail_quote">2011/11/22 Chris Benham <span dir="ltr"><<a href="mailto:cbenhamau@yahoo.com.au">cbenhamau@yahoo.com.au</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div><div style="color:#000;background-color:#fff;font-family:times new roman,new york,times,serif;font-size:12pt"><div><span>Forest,</span></div><div class="im">
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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><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><div class="im">
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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><div><span>The FBC doesn't stipulate that all the voters use "optimal strategy", so that isn't relavent.<br></span></div>
<div><span><a href="http://wiki.electorama.com/wiki/FBC" 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" target="_blank">http://nodesiege.tripod.com/elections/#critfbc</a><br><br>Chris Benham<var></var></span></div>
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</div><b><span style="FONT-WEIGHT:bold">From:</span></b> "<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>" <<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>><br>
<b><span style="FONT-WEIGHT:bold">To:</span></b> C.Benham <<a href="mailto:cbenhamau@yahoo.com.au" target="_blank">cbenhamau@yahoo.com.au</a>> <br><b><span style="FONT-WEIGHT:bold">Cc:</span></b> em <<a href="mailto:election-methods@electorama.com" target="_blank">election-methods@electorama.com</a>>; MIKE OSSIPOFF <<a href="mailto:nkklrp@hotmail.com" target="_blank">nkklrp@hotmail.com</a>> <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><div><div class="h5"><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>
> <a href="http://electorama.com/2005-June/016410.html" target="_blank">electorama.com/2005-June/016410.html</a><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></div></div></div><br>----<br>
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