[EM] Your opinion on being able to vote no preference?

[Alex Small]

Forest Simmons said:
> For example, MinMax(pairwise opposition) satisfies the FBC when equality
> at the top is allowed.  This method chooses as winner the candidate
> whose maximum pairwise opposition is minimal.
...
> As near as I can tell this is the simplest deterministic pairwise method
> that satisfies the FBC.

I wonder if it's possible to satisfy weak FBC with Condorcet methods that
allow equal rankings.  Although it's a method that uses only pairwise
information, MinMax(pairwise opposition) does not always elect the
Condorcet Winner.  Consider the following series of pairwise contests:

A>B:  45:44
B>C:  52:48
A>C:  51:49

Maximum pairwise opposition for each candidate
A:  49
B:  48
C:  52

MinMax(pairwise opposition) would select B as the winner, while any
Condorcet method would select A.

My suspicion is that you can never satisfy even weak FBC with Condorcet
methods.  Every Condorcet method needs a "backup" to handle the case when
nobody wins all of his pairwise contests.  If the auxillary method picks
your least favorite, and your compromise pairwise beats all candidates
except your favorite, you have an incentive to rank compromise ahead of
favorite.  Your compromise is then the Condorcet winner, a situation that
you prefer to seeing your least favorite win with the backup method.

That obviously isn't a proof, but it is a sketch of the basic problem with
FBC (weak or strong) and Condorcet methods.