Not only is SSFC attainable at that price, but so is this more ambitious criterion:
Strong Sincere Strategy Criterion (SSSC):
If a majorilty prefer X to Y, and vote sincerely, then Y shouldn't win.
[end of SSSC definition]
Here's a method that meets SCCC and SFCC (any method that meets SSSC meets SFCC):
Ranked Majority Defeat Disqualification (RMDD):
Balloting: Rank balloting The voter may rank as many candidates as s/he wants to. Equal rankings and truncation are allowed.
A candidate loses if a majority vote another candidate over hir.
[end of RMDD definition]
As I define sincere voting, and with RMDD's balloting, anyone who prefers X to Y and votes sincerely votes X over Y.
And so if a majority prefer X to Y and vote sincerely, then, by RMDD's rules, Y loses.
But RMDD is indecisive. It can return a tie in which there are several winners, or a tie in which there are zero winners. Of course a tiebreaker could be used, but if a 0-winner tie is solved and someone is elected, then SSSC compliance is lost. Since the method can't identify a CW who has a defeat, SSFC complilance is lost too.
That's also why we can't define a method that says: Any candidate with a majority defeat by the CW loses.
The method has no way of identifying a CW who has a defeat.
But does that mean that if we insist on a winner, SSFC compliance is unattainable? Maybe not. Though the method's rules can't specifically refer to the CW, that doesn't mean that a method can't meet a criterion that refers to the CW. SFC and (my) CC show that.
So, can anyone show that SSFC is unattainable if we insist on a winner? Or suggest a method that might meet SSFC and always returns a winner?
Let me repeat the definition of SSFC here:
If a majority prefer the CW to Y, and vote sincerely, then Y shouldn't win.
[end of SFCC definition]
That's SFC, without the clause "If no one falsifies a preference...".
Compliance with SSFC would mean that a method is strategy-free, for a majority, for protecting the CW's win from being taken by a less-liked other candidate, without having to stipulate that no one falsifies a preference.
Mike Ossipoff
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