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

[Forest Simmons]

There is a folk theorem about the impossibility of the Strong Favorite
Betrayal Criterion.  In other words, any method that doesn't allow
equality in the top position of the ballot will give incentive to betray
favorite in some situations.

On the other hand some methods that allow equal ranking in the top
position satisfy the (weak) FBC.

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.

Suppose that candidate X is this MinMax candidate and that some candidate
Y is ranked ahead of X on N ballots, but no candidate Z is ranked ahead of
X on more than N ballots.  Then, by definition, for any other candidate V,
there is a candidate W, such that W is ranked ahead of V on more than N
ballots.

In this method ranking Compromise ahead of Favorite (rather than equal to
Favorite) could increase Favorite's max pairwise opposition, but could not
decrease Compromise's max pairwise opposition.  In other words, it doesn't
increase Compromise's chance of winning against anybody except Favorite.
Therefore there is no incentive for this insincere rank reversal.

As near as I can tell this is the simplest deterministic pairwise method
that satisfies the FBC.

Forest

On Mon, 24 Feb 2003, Tom McIntyre wrote:

> Folks, sorry if this has been discussed, but I'm getting nowhere looking
> for it in the Yahoo archives (if it's in there, please just point me to it).
>
> I know this group is familiar with the concept of allowing voters, under
> condorcet, to vote ties, such as A and B are equal, but both preferred to C:
>
> A=B>C
>
> I know I've seen examples of this.  The alternatives are to enforce
> strict ranking of the candidates the voter chooses to list, or to
> enforce strict ranking of all candidates on the ballot.  I've seen some
> discussion of the relative pros and cons on the condorcet.org site
> ("inc.html"), but I'd like to know if there's consensus here on which of
> these alternatives would be better in actual practice.
>
> As I stated before, if it's already been discussed, please just point me
> to the postings.
>
> Thank you,
> Tom McIntyre
>
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