Markus--
Not only does Plurality pass your "SDSC", but BeatpathWinner fails it:
AB51, BC52, CA52
B wins in BeatpathWinner, though more than half of the voters have ranked A over B.
Your critrerion only applies if votes are "admissible". I don't know what "admissible" means, but, by any reasonable definition of it, my example above doesn't require inadmissible ballots.
A long time ago I read the definition of an "admissible" ballot, but I haven't used that term, and have rerely if ever encountered it in discussion. Though I haven't had time to get to a university library to look for it there, I looked for that definition on the Internet, but didn't find it.
But, whatever "admissible" means, Pluralitly still passes your "SDSC", because your admissibility stipulation can only disqualify a failure example. You said that if more than half of the voters rank y over x thern x shouldn't win. If more than half of the voters vote for y then it's quite impossible for x to win in Plurality.
Abouit the issue of what "ranking y over x" means in Plurality, I discussed that in my previous message about this.
Is a ballot "admissible" iff it conforms to the method's balloting rules and isn't a dominated strategy for the person who voted that ballot?
If so, then your criterion is about sincere preferences, because dominated strategy is defined in terms of sincere preferences. You'd said that critreria shouldn't involve sincere preerence.
When I say "your SDSC", I'm referring here to the one that I replied about yesterday. I don't know if you've proposed another one since then, because I haven't checked the postings yet.
Anyway, as I said, can you or can you not write a votes-only criterion (nothing to do with preferences) that is equivalent to my Condorcet's Critrerion. Or, if you prefer, equivalent to SDSC?
Let me steate my Condorcet's Criterion here:
If there's a CW, and if everyone votes sincerely, then the CW should win
[end of CC definition]
A voter votes sincerely if s/he doesn't falsify a preference or fail to vote a preference that the balloting system in use would have allowed him/her to vote in addition to the preferences that s/he actually did vote.
[end of sincere voting definition]
Strong Defensive Strategy Criterion (SDSC):
If more than half of all the voters prefer X to Y, then they should have a way of voting that ensures that Y won't win, without any member of that majority voting a less-liked candidate equal to or over a more liked candidate.
[end of SDSC definition]
A voter votes X equal to Y if s/he votes X over someone, and votes Y over someone, but doesn't vote X over Y and doesn't vote Y over X.
A voter votes X over Y if, should we count only his/her ballot, with everyone but X & Y deleted from it, X would be the unique winner.
[end of 2 voting definitions]
Mike Ossipoff
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