Warren Smith wrote:
"SFC: If no one falsifies a preference, and there's a CW, and a
majority of all the voters
prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win."
I must say, SFC is then rather silly.
It says "if no one falsifies a preference" redundantly since it also says
"a majority of all the voters prefer the CW to candidate Y"
(of course they do, that followed from defn of CW and fact nobody falsified a
preference)
and redundanty it also says "and vote sincerely" (of course they do, since
nobody falsified a preference)
The criterion refers to all sincere preferences, and by "falsifies" it
means order-reverse and not just truncate or
otherwise falsely equal-rank. It is about a faction whose favourite Y
isn't the sincere CW not being able to elect Y
just by truncating.
So say sincere is
43: A>B
10: B>A
10: B>C
37: C>B
B is the CW, so "there's a CW". If the A supporters truncate
43: A
10: B>A
10: B>C
37: C>B
Now C>B>A>C, but no-one has "falsified" a preference and more than
half the voters ("a majority")
have "voted sincerely" expressing their preference for the (sincere)
"CW"(B) over "Y" (A in this example,
B>A 57-43), so the criterion says that in this scenario A mustn't win.
This isn't the same as the Condorcet criterion, because
BP/RP/MM/River(Margins) and Smith/Schwartz,IRV
all meet Condorcet but elect A.
I speculate that the reason for the confusing unusual language is to do
with Mike's long-running propaganda
war in favour of Winning Votes and Approval versus Margins and IRV.
My stab at making it clearer and more "technical":
"If more than half the voters vote X over Y and it is possible to
complete truncated ballots in a way to
make X the CW, then Y must not win."
Chris Benham
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