I've posted a precise definition of "prefer", but actually it doesn't matter
what "prefer" means. In fact it doesn't matter if "prefer" means anything,
for the purpose of my criteria.
Some or all of my criteria use the word "prefer", as do some of their
First, let me state some of those supporting definitions:
A voter votes X over Y if he votes in such a way that if we count only
his/her ballot, as if there were no other ballots, and disregard the other
ballots, and if all candidates other than X and Y are deleted from that
ballot, and the count is conducted as if candidates other than X and Y were
never in the election, then X wins and Y doesn't win.
[end of definition of voting X over Y]
A preference is an instance of preferring.
To vote a preference for X over Y means to vote X over Y when preferring X
To falsify a preference means to vote a preference for X over Y when one
doesn't prefer X to Y.
Definition of sincere voting:
A voter votes sincerely if s/he doesn't falsify a preference, or fail to
vote every 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 definition of sincere voting]
Now, as an example, I'll re-state my definition of SFC:
If no one falsifies a preference, and if a majority prefer X to Y and vote
sincerely, then Y shouldn't win.
[end of SFC definition]
Now, demonstrations that a method meets or fails SFC are just as valid no
matter what "prefer" means. To see that, substitute, for "prefer" in all of
the definitions above, any verb you like. It could be a nonsense word. I
suggest that you use one from Lewis Carroll.
When you do that, you'll find that demonstrations that, for a particular
method, an SFC failure example can or cannot be written are just as valid,
regardless of what nonsense word you substitute for "prefer".