<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">I think you have wandered into the realm of sophistry. Yes, if the voters are constrained to two<BR>rating or preference levels then Approval meets "2-slot Condorcet", barring exact pairwise ties<BR>"2-slot Condorcet" is decisive, and since Approval meets the FBC then compliance with FBC</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">and "2-slot Condorcet" are compatible.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">But when we talk about the Condorcet criterion it is generally understood that there are more</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">than 2 candidates and that the voters are free to give full strict rankings (which isn't possible on</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">2-slot ballots).</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">I'm happy with the concept "n-slot Condorcet" (where n is 3 or greater) meaning that if we assume<BR>that no voter wanted to express more than n number of preference-levels and they all expressed</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">their sincere rankings then a sincere CW must win.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">(So, I think the 3-slot version of your suggested "RCW" method is a promising "3-slot Condorcet"</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">method.)<VAR id=yui-ie-cursor></VAR></SPAN></div>
<div><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">"Indeed, the three slot case does appear to satisfy the FBC as well."<BR><BR>Isn't there a "not" missing from that sentence?</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">"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."</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">The main "practical purpose" of the FBC as I see it is to assist in marketing the method by giving</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">voters an absolute guarantee. Also, as you suggest by capitalizing, that is a big "if". <BR></SPAN><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">The strength of a voter's incentive to submit an approval-like ballot will depend on their sincere</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">ratings (or utilities) and how well informed they are (about say which candidates are the front-runners).</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">So do voters who don't know who the front-runners are and whose sincere ratings are evenly </SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">spaced have an incentive to only use the Top and Bottom ratings slots? If so, it would be much</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">weaker than it is with Range.</SPAN><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Chris Benham</div></SPAN>
<div style="RIGHT: auto"><BR 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> "fsimmons@pcc.edu" <fsimmons@pcc.edu><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> em <election-methods@electorama.com>; MIKE OSSIPOFF <nkklrp@hotmail.com> <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 <BR>> simply Approval, which does satisfy the <BR>> FBC."<BR>> <BR>> When you introduced the method you suggested that 3-slot ballots <BR>> be used "for simplicity".<BR>> I thought you might be open to say 4-6 slots, but a complicated <BR>> algorithm on 2-slot ballots<BR>> that is equivalent to Approval ??<BR>> <BR>>
"Now consider the case of range ballots with three slots: and <BR>> suppose that optimal strategy requires the <BR>> voters to avoid the middle slot. Then the method reduces to <BR>> Approval, which does satisfy the FBC."<BR>> <BR>> The FBC doesn't stipulate that all the voters use "optimal <BR>> 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>> <BR>> <BR>> <BR>> <BR>> <BR>> <BR>> ________________________________<BR>> From: "<A href="mailto:fsimmons@pcc.edu" ymailto="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</A>" <BR>> To: C.Benham <BR>> Cc: em ; MIKE OSSIPOFF <BR>> <BR>> Sent:
Tuesday, 22 November 2011 11:11 AM<BR>> Subject: Re: An ABE solution<BR>> <BR>> <BR>> <BR>> From: "C.Benham" <BR>> <BR>> > <BR>> > Forest Simmons, responding to questions from Mike Ossipff, <BR>> 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 <BR>> 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 <BR>> 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 <BR>> 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 <BR>> 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 <BR>> Approval, which does satisfy the <BR>> FBC. Does Approval satisfy the Condorcet Criterion? I would <BR>> say no, but it does satisfy the "votes only <BR>> Condorcet Criterion." which means that the Approval winner X <BR>> pairwise beats every other candidate Y <BR>> according to the ballots, i.e. X is rated above Y on more <BR>> ballots than Y is rated above X.<BR>> <BR>> Now consider the case of range ballots with three slots: and <BR>> suppose that optimal strategy requires the <BR>> voters to avoid the middle slot. Then the method reduces to <BR>> 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 <BR>> 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 <BR>> be <BR>> > the case<BR>> > > that increasing the votes for A over B in the pairwise <BR>> 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 <BR>> 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 <BR>> Order) is needed in addition to the <BR>> pairwise matrix; the covering information comes from the <BR>> 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 <BR>> the pairwise matrix? If so, then this is a <BR>> counterexample to the last quoted sentence above in the <BR>> attempted proof of the incompatibility of the CC <BR>> and the FBC.<BR>> <BR>> Forest<BR><BR><BR></DIV></DIV></div></body></html>