<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>Kathy,</DIV>
<DIV> </DIV>
<DIV>Imagine that Approval is used to elect the US President and </DIV>
<DIV>as in the current campaign the Republicans are fielding one</DIV>
<DIV>candidate, McCain. Does that mean that the big fight for the</DIV>
<DIV>Democrat nomination between Clinton and Obama we've just</DIV>
<DIV>seen would in the Approval scenario be completely unnecessary?</DIV>
<DIV> </DIV>
<DIV><BR>Why not simply endorse both candidates? After all, one cannot</DIV>
<DIV>possibly spoil the election for the other because Approval has</DIV>
<DIV>no spoiler problem. Voters simply approve candidates or not</DIV>
<DIV>completely regardless of what other candidates are on the ballot,<BR>right?</DIV>
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<DIV><BR> </DIV>
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<DIV>I think that in practical effect Approval does have a "spoiler" or</DIV>
<DIV>split-vote problem that would be sufficient for the Democrats to</DIV>
<DIV>still want to endorse one candidate only.<BR><BR></DIV>
<DIV> </DIV>
<DIV>What I actually wrote in my initial post on the 5 "fairness</DIV>
<DIV>principles in your paper (regarding IIA):<BR></DIV>
<DIV> </DIV>
<DIV>In practical effect *no* method meets this.Approval and Range can be said to meet <BR>Independence of Irrelevant Alternatives (IIA) only if the votes are interpreted as the voters giving <BR>ratings on some fixed scale that is independent of the actual candidates. <BR><BR>On this perverse interpretation Approval and Range do not reduce to FPP in the 2 candidate election,<BR>in violation of Dopp's "fairness principle 4":<BR><BR>"Any candidate who is the favorite [first] choice of a majority of voters should win."</DIV>
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<DIV>(approval or non-approval counts as "rating" on a 2-point scale).<BR></DIV>
<DIV> </DIV>
<DIV>This latter point you seem to implicitly acknowledge in one of your recent posts:</DIV>
<DIV> </DIV>
<DIV><BR>"In actuality, if these are the same voters both before and after you<BR>add another candidate C, then your first example with two candidates,<BR>to be consistent with your second example with three candidates should<BR>be:<BR><BR>25 A<BR>40 AB<BR>35 B<BR><BR>so that B wins in the first example AND in the second when another<BR>candidate is introduced."</DIV>
<DIV> </DIV>
<DIV><BR><BR>Chris Benham<BR></DIV>
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<DIV><BR><BR> </DIV></div><br>
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