[EM] Uncountable Ballot

[Forest Simmons]

On Wed, 7 May 2003, [iso-8859-1] Kevin Venzke wrote:

>  --- josh at narins.net a écrit :
> > I still think its a better ballot for the reason that no voter ever has
> > to compare any two candidates they do not want, and it allows for a much
> > fuller expression of voter desire.
>
> Why do you think so?  The only added ability for the voter is to create
> a cycle on his own ballot.  If the voter can't resolve A>B>C>D>E>A>B>C...,
> then maybe he should just rank them equal on a standard ranked ballot.
> I think on such ballots equal rankings mean "don't know" more likely than
> "don't care," anyway.

Actually, the difference between don't know and don't care could be
discerned on this type of ballot: a blank could mean don't care, and a
question mark could mean don't know.

Also, it may be that some methods distinguish between cycles in one
direction and cycles in another.  For example, A>C>B>A would cancel
A>B>C>A in most methods, but three cycles in the second direction might be
counted as one each of A>B>C, B>C>A, and C>A>B,  which do not cancel each
other out automatically in most reputable pairwise methods, although they
do effectively cancel each other in Borda.

The physicist in me says that a cycle contributes "torsion" to the
distribution of votes.

>
> Here's another idea for a 2D ballot: have a grid, maybe of hexagons, and
> ask the voter to plot all the candidates as well as himself somewhere in
> the grid, lower distance corresponding to similarity.  Average all the
> ballots somehow and elect the candidate closest to the "center of gravity"
> of the voters.
>
> It would be messy, I think, but I think people might be less inclined to
> "bullet vote" on such a ballot.

I see, each voter projects issue space onto the plane spanned by the two
issues that are most important to the voter, and locates self and
candidates in that two dimensional projection.

Then (for example) the election method would estimate (from all of these
projections) the candidate and voter locations in some (reconstructed)
full blown issue space, and elect the candidate minimizing the average
distance to the voters.

Nice idea!

Forest