[EM] a method based on candidate separation

[Forest Simmons]

Mike,

I like your idea of using candidate separation as a measure of defeat
strength in MAM ... not for public proposal, of course, but for polling
purposes, as you point out.

When the number of candidates is not too great the polled members of the
electorate could be asked to indicate (for each pair of candidates) if
their separation was above average.  Then each pair gets a separation score
which is just the number of polled voters who thought their separation was
above average.

Note that the poll questionnaire could be in the form of a matrix.  the
voter puts a one in the space in row i and and column j is they think that
the separation of candidate i and candidate j is above average.  [Actually,
since the matrix would be symmetrical, half of the entries would be
redundant.]

An indirect consistency check on the accuracy and sincerity of these
estimates could be made as follows:  (1) have each polled voter also
indicate who their favorite candidate was. (2) for each candidate X, let
A(X) be the average of the filled out poll matrices of the supporters of
X.  (3) Estimate the separation between candidate X and candidate X' as the
Hamming distance between the matrices A(X) and A(X').

In other words, the candidate separations should be reflected in the
disparity of responses of their respective supporters.

In fact,the pair of candidates with the most separation should have
supporters with the greatest difference in their pattern of responses even
if the questions are not about candidate separations per se.

This fact can be used to find candidate separations even when there are
many candidates.  Just have the voters respond to thirty agree/disagree
statements along with who is their favorite candidate, and use the
differences in supporter responses to estimate the relative separation of
the candidates.

One caveat:  One must try to make the statements on the questionnaire as
independent of each other as possible, so that we don't have "clone
questions" in disguise.  And since it is impossible to come up with
statements with zero correlation responses, the correlations must be taken
into account either explicity or implicity.

To make the difficulty more clear, suppose that twenty of the thirty
questions were just re-wordings of the first question.  Then whatever issue
the first question represented would get undo weight in the separation
computation, unless the total weight of the first twenty questions were
reduced once the correlation was detected.

This is very similar to the basic problem of taxonomy in which all kinds of
measurements of various species are made as a basis for classification.
Many of those measurements will turn out to be redundant.  The problem is
how to filter out the redundancy so that the redundant measurements don't
distort the classification scheme.

In general it is a problem of pattern recognition, and has been solved in
many contexts already by "singular value decompositions" and the like, so
we don't need to re-invent the wheel.  Still there may be some quick and
dirty way especially appropriate for our application.

For example each polled voter could indicate which of the thirty statements
they considered most important. Then in the hamming distance computation
each question could be weighted by its average estimated importance.  A
cloned question would have its importance spread among the clones, etc.

It's fun to think about!

Forest




On Tue, Jun 3, 2014 at 8:11 AM, Michael Ossipoff <email9648742 at gmail.com>
wrote:

>
>
> On Fri, May 23, 2014 at 6:34 PM, Forest Simmons <fsimmons at pcc.edu> wrote:
>
>> Ross Hyman recently suggested a method that eliminates the pairwise loser
>> of the bottom remaining candidates on a list (in his suggestion the list
>> was a random ballot order) as long as there remain two or more uneliminated
>> candidates.
>>
>
> Isn't that Sequential-Paiwise (SP), the method recmmended in Robert's
> Rules, and used often in meetings and legislatures?
>
> I recommend SP for meetings where quick show-of-hands voting is desired,
> and where amicable conditions exist. For that purpose, I like it because it
> meets the Smith Criterion, which implies MMC and Condorcet, especially
> useful in an amicable electorate not subject to chicken-dilemma.
>
>
>>
>>
>> It got me to thinking that ideally we would eliminate the pairwise loser
>> of the two candidates with the most separation in issue space.
>>
>
> Yes, interestng suggestion. And that measure of importance of pairwise
> defeats could be applied to other methods too, including Condorcet methods.
> For example, it suggests a version of MAM that measures defeat-strength by
> candidate-separation.
>
> As you point out, candidate-separaton is difficult, but not impossible, to
> measure.
>
>
>
>
>
>
>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> I don't suggest this as another public proposal, but for use as a
>> standard of comparison like MAM, when range style ballots are used.
>>
>>
> Yes, MAM, SP(candidate-separation), or MAM(candidate-separation) could be
> used as a comparison-standard, for that pre-election poll, where
> comparison-standard-winner is reported, and also is reported the way of
> voting that would elect that winner in the binding election's method (e.g.
> Benham) at Nash Equilibrium.
>
> Michael Ossipoff
>
>
>
>>  Forest
>>
>>
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list
>> info
>>
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20140603/b74888ab/attachment-0002.htm>