[EM] Toy election model: 2D IQ (ideology/quality) model

[Kathy Dopp]

> There have been attempts to find out the number of dimensions in opinion
> space by looking at dimensions alone. Most of these have used principal
> components analysis to align the greatest variety along one axis, the
> greatest among the remaining to another, and so on.

I would allow for any number of dimensions corresponding to factors
voters may take into consideration and would not use any analysis that
tried to obtain one formula or description applying to all voters.

>
> To my knowledge, these have generally found somewhere between one and two
> dimensions. However, at least for the examples I gave in my reply to David's
> post, these have been done in countries that use FPTP, and FPTP's relative
> failure to handle more than two parties could be affecting the way in which
> people consider their opinions, squeezing those opinions to fit along a line
> and thus reducing the dimensionality.
>
> Also, if one relaxes the requirement that each axis should "mean" something
> (e.g. left-vs-right, centralized-vs-decentralized, pragmatic-vs-idealist),
> then metric multidimensional scaling would work better than PCA (I think).
> It would be interesting to take some political data, such as survey
> responses or legislature voting records, define a distance between these
> (Euclidean, for instance, or Hamming in the case of aye/nay), and then try
> to reconstruct a lower-dimensional space focusing only on making the model
> distances as close to the reported distances as possible.

The survey methods would have to be slightly altered to do what I have
in mind, which is to allow for individual differences rather than
trying to make broad brush findings that don't fit more than 60 to 70%
of the population.

I totally agree with taking multi-dimensional measurements and then
reconstructing a lower dimensional space to represent voter and
candidate relative positions.  I would use Euclidean geometry to do
this.

You are motivating me to write up my ideas and publish them online
soon -- when I find time -- perhaps after Xmas.



-- 

Kathy Dopp
http://electionmathematics.org
Town of Colonie, NY 12304
"One of the best ways to keep any conversation civil is to support the
discussion with true facts."
"Renewable energy is homeland security."

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

View some of my research on my SSRN Author page:
http://ssrn.com/author=1451051