[EM] ICT definition. Presumed Kemeny definition.
Kevin Venzke
stepjak at yahoo.fr
Mon Apr 23 15:34:23 PDT 2012
Hi Mike,
>ICT definition:
>
>(as described by Chris Benham, unless I've made an error)
>
>Iff the number of voters ranking X over Y, plus the number of voters equal-top-rating X and Y, is greater than the
>number of voters ranking Y over X, then X "beats" Y.
>
>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
>I say "beat" (with or without the quotes), I mean it in the above-defined sense.
>
>If there's exactly one beats-all candidate (candidate who beats all of the others), then s/he wins.
>
>If not, then the winner is the beats-all candidatate who is ranked in 1st place on the most ballots.
>
>[end of ICT definition]
>
>As I said, ICT meets FBC, and is defection resistant. Maybe so defection-resistant as to be called defection-proof.
>
>If Kevin &/or Chis are listening right now, I have a question:
>
>What if, instead of defining "beat" as above, I said:
>
>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
>to the number of voters ranking Y over X.
>
>If there is exactly one candidate not beaten by anyone, then s/he wins.
>
>Otherwise, the winner is the unbeaten candidate who is ranked in 1st place on the most ballots
>
>[end of questioned alternative definition of ICT]
>
>Would that still meet FBC and be defection-resistant? Would it lack some other desirable property,
>or acquire some undesirable property?
>
I haven't looked at ICT really. But your revised wording is how ICA is worded. It directs you to look
for a single unbeaten candidate. I think it sounds better to say you're picking the winner from among the
undefeated candidates, than from among the candidates who defeated everybody including each other.
I'm pretty sure your definitions are identical... Unless I'm missing something really obvious.
Kevin
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