<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">Hi Mike,<BR class=yui-cursor style="RIGHT: auto"></SPAN></div>
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<DIV dir=ltr style="RIGHT: auto"><BR>ICT definition:<BR><BR>(as described by Chris Benham, unless I've made an error)<BR><BR>Iff the number of voters ranking X over Y, plus the number of voters equal-top-rating X and Y, is greater than the <BR>number of voters ranking Y over X, then X "beats" Y. <BR><BR>Of course that's a very weak meaning for "beat", and it's possible for X and Y to both beat eachother in that sense. Of course, when<BR>I say "beat" (with or without the quotes), I mean it in the above-defined sense.<BR><BR>If there's exactly one beats-all candidate (candidate who beats all of the others), then s/he wins.<BR><BR>If not, then the winner is the beats-all candidatate who is ranked in 1st place on the most ballots.<BR><BR>[end of ICT definition]<BR><BR>As I said, ICT meets FBC, and is defection resistant. Maybe so defection-resistant as to be called defection-proof.<BR><BR>If Kevin &/or Chis are listening right now, I have a
question:<BR><BR>What if, instead of defining "beat" as above, I said:<BR><BR>X is unbeaten by Y iff the number of voters ranking X over Y, plus the number of voters equal-top-ranking X and Y, is at least equal<BR>to the number of voters ranking Y over X.<BR><BR>If there is exactly one candidate not beaten by anyone, then s/he wins.<BR><BR>Otherwise, the winner is the unbeaten candidate who is ranked in 1st place on the most ballots<BR><BR>[end of questioned alternative definition of ICT]<BR><BR>Would that still meet FBC and be defection-resistant? Would it lack some other desirable property,<BR>or acquire some undesirable property?</DIV>
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<DIV style="FONT-SIZE: 12pt; RIGHT: auto; FONT-FAMILY: times new roman, new york, times, serif">I haven't looked at ICT really. But your revised wording is how ICA is worded. It directs you to look</DIV>
<DIV style="FONT-SIZE: 12pt; RIGHT: auto; FONT-FAMILY: times new roman, new york, times, serif">for a single unbeaten candidate. I think it sounds better to say you're picking the winner from among the</DIV>
<DIV style="FONT-SIZE: 12pt; RIGHT: auto; FONT-FAMILY: times new roman, new york, times, serif">undefeated candidates, than from among the candidates who defeated everybody including each other.</DIV>
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<DIV style="FONT-SIZE: 12pt; RIGHT: auto; FONT-FAMILY: times new roman, new york, times, serif">I'm pretty sure your definitions are identical... Unless I'm missing something really obvious.</DIV>
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<DIV style="FONT-SIZE: 12pt; RIGHT: auto; FONT-FAMILY: times new roman, new york, times, serif">Kevin</DIV>
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