[EM] Vote Management

[Forest Simmons]

On Thu, 10 Apr 2003, Alex Small wrote:

> It seems that this phenomenon of figuring out how many candidates to run
> is a common feature of PR systems that focus on candidates rather than
> parties.  Cumulative Voting, Limited Voting, and STV all come to mind off
> the top of my head.
>
> Party list systems, even open-list systems, suffer from no such defect.

[big snip]

>
> Anyway, I'm curious if anybody can name other systems with few "vote
> management" issues.
>

Candidate Proxy is the simplest such method from the voter point of view.
All of the vote management worries are postponed to the proxy stage.

At this stage ...
(1) the proxies have a good idea of their relative strengths, and
(2) they can do the calculations with the help of their advisors.

A more complicated system that requires minimal vote management is the
voter space method that I proposed in a 20 March 2003 posting entitled
"Another PR Method Based on Ranked Ballots."

It simply locates the candidates in voter space according to the ballot
profiles of the candidates' supporters, and then selects the subset of
candidates whose maximal Voronoi sum is minimal.

For complete details see that posting.  Here is a partial explanation:

Each candidate has a Voronoi region relative to each subset of
candidates.

A Voronoi (or Dirichlet) region is the set of points (voters in voter
space) that form the natural neighborhood of one point (candidate)
relative to some discrete subset of points (candidates), i.e. the voters
that are closer to the given candidate than to any of the other candidates
in the subset.

The Voronoi sum is the sum of distances from the given candidate to the
voters in the region.  The precise properties of the method depend on
which metric is used for calculating this distance as well as which metric
is used for determining the Voronoi regions. These two metrics could be
different.

If the discrete metric [ d(A,B)=0 or 1, depending on whether or not A and
B are equal ] is used for the Voronoi sum calculation, then we are just
minimizing the maximum number of voters per Voronoi region, without taking
into account how well they are represented on average within that region.

For this method to work there has to be some way of projecting the
candidates into voter space.  One way to do this is to average all of the
ballots that give maximal support to the candidate being projected.

Obviously this method cannot be used by itself when there are too many
subsets to compare.

Forest