Here are my "votes-only" definitions:
SFC: If X beats all other candidates in pairwise comparisons, and a majority of ballots rank X over Y, then Y does not win.
GSFC: If X is in the Smith set and Y is not, and a majority of ballots rank X over Y, then Y does not win.
SDSC: For any combination of N ballots that all rank candidate X over candidate Y, and any other combination of M ballots, if N is greater than M, then Y does not win the election when the two groups of ballots are combined.
Note: The statement in the electionmethods.org commentary that "Compliance with SDSC means that a majority never needs any more than truncation strategy to defeat a particular candidate" is puzzling (truncation strategy is "falsely voting two candidates equal", is it not?). Also, the statements in the commentary about "countering offensive order reversal" are completely irrelevant, since the need for defensive strategy is based on the opposing votes cast regardless of whether those votes are the result of offensive order reversal.
WDSC: For any combination of N ballots that all rank candidate X equal to or higher than candidate Y, and any other combination of M ballots, if N is greater than M, then Y does not win the election when the two groups of ballots are combined.
FBC: For some set S of ballots, if R is the set of results that can occur when ballot B is added to S if candidate X is given the highest ranking on B, and R' is the set of results that can occur if ballot B is added to S when candidate X is not given the highest ranking on B, then either X is a member of R, or R' is a subset of R.
-- Richard
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