[EM] Majority Potential

[Forest Simmons]

Here's an idea on how to use Richard's "Majority Potential" idea in an
actual election.

On each ballot ...

(1) Have the voter select three issues from an exhaustive list.

(2) Have the voter declare for or against the statement of the issue.

(3) Have the voter assess the relative importance of the three issues.

(4) Have the voter estimate the stance of each of the candidates on each
of the three issues. 


I've left out the "how to" part of eliciting this information from
the voter, because I want to get right to the part that is more
interesting to me.

>From the information on each ballot construct two arrays W and C.
[You can call this the WC method if you want :-]

W is a one by n array, where n is the number of issues in the
comprehensive list.  The only non-zero entries are the three signed
weights corresponding to the three issues considered most important by the
voter of the ballot. The absolute values of the weights sum to unity. The
signs correspond to agreement or disagreement with the statement of the
issue.

C is an n by m array, where n is the number of issues and m is the number
of candidates. Each row corresponds to an issue, and each column
corresponds to a candidate. The numbers in a particular column are the
voter's estimates of that column's candidate's stances on the issues. No
entry of matrix C has an absolute value greater than 100%.

An entry of C is positive or negative depending on whether the voter
estimates that the candidate generally agrees or disagrees with the
statement of the issue (not according to whether the candidate agrees with
the voter).

The absolute value of the entry is the voter's estimate of the candidate's
ability to affect the issue one way or another if elected.

The matrix product WC is a one by m array from which the voter's ranking
of the candidates can be fairly estimated.

Now augment the matrix C with columns corresponding to idealized
candidates uniformly distributed on all of the issues. Call this augmented
matrix C'.

Then WC' is an array from which the voter's rankings of all of the
candidates, real and idealized, can be deduced (more or less).

Apply Copeland's method to these rankings.

Forest