<html><head><style type="text/css"><!-- DIV {margin:0px;} --></style></head><body><div style="font-family:times new roman, new york, times, serif;font-size:12pt"><DIV>Forest,<BR>Given IRV's compliance with the "representativeness criteria" Mutual Dominant Third, Majority for<BR>Solid Coalitions, Condorcet Loser and Plurality; why should the bad look of its "erratic behaviour"<BR>be sufficient to condemn IRV in spite of these and other positive criterion compliances such as</DIV>
<DIV>Later-no-Harm and Burial Invulnerability?</DIV>
<DIV><BR>"....in the best of all possible worlds, namely normally distributed voting populations in no more <BR>than two dimensional issue space."</DIV>
<DIV><BR>Why does that situation you refer to qualify as "the best of all possible worlds" ?</DIV>
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<DIV>Chris Benham</DIV>
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<DIV><BR>Forrest Simmons wrote (Wed. Nov.26):</DIV>
<DIV>Greg,<BR><BR>When someone asks for examples of IRV not working well in practice, they are usually protesting against <BR>contrived examples of IRV's failures. Sure any method can be made to look ridiculous by some unlikely <BR>contrived scenario.<BR><BR>I used to sympathize with that point of view until I started playing around with examples that seemed natural <BR>to me, and found that IRV's erratic behavior was fairly robust. You could vary the parameters quite a bit <BR>without shaking the bad behavior.<BR><BR>But I didn't expect anybody but fellow mathematicians to be able to appreciate how generic the pathological <BR>behavior was, until ...<BR><BR>... until the advent of the Ka-Ping Lee and B. Olson diagrams, which show graphically the extent of the <BR>pathology even in the best of all possible worlds, namely normally distributed voting populations in no more <BR>than two dimensional issue space.<BR><BR>These diagrams are not
based upon contrived examples, but upon benefit-of-a-doubt assumptions. Even <BR>Borda looks good in these diagrams because voters are assumed to vote sincerely.<BR><BR>Each diagram represents thousands of elections decided by normally distributed sincere voters.<BR><BR>I cannot believe that anybody who supports IRV really understands these diagrams. Admittedly, it takes <BR>some effort to understand exactly what they represent, and I regret that the accompaning explanations are <BR>too abstract for the mathematically naive. They are a subtle way of displaying an immense amount of <BR>information.<BR><BR>One way to make more concrete sense out of these diagrams is to pretend that each of the "candidate" <BR>dots actually represents a proposed building site, and that the purpose of each simulated election is to <BR>choose the site from among these options.<BR><BR>Each of the other pixels in the diagram represents (by its color) the
outcome the election would have (under <BR>the given method) if a normal distribution of voters were centered at that pixel.<BR><BR>So each pixel of the diagram represents a different election, but with the same candidates (i.e. proposed <BR>construction sites).<BR><BR>Different digrams explore the effect of moving the candidates around relative to each other, as well as <BR>increasing the number of candidates.<BR><BR>With a little practice you can get a good feel for what each diagram represents, and what it says about the <BR>method it is pointed at (as a kind of electo-scope).<BR><BR>On result is that IRV shows erratic behavior even in those diagrams where every pixel represents an election <BR>in which there is a Condorcet candidate.<BR><BR>My Best,<BR><BR>Forest<BR> <BR><!--htdig_noindex--></DIV></div><br>
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