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

[Forest Simmons]

Alex, I	think you are right.

For example, although MinMax(pairwise opposition) satisfies the FBC, the
minute you restrict it to the Smith set it no longer satisfies the FBC,
since you might have to favor Compromise over Favorite to get it into the
Smith set.

Forest

On Wed, 19 Mar 2003, Alex Small wrote:

> 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.
>
>
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