> From: Jameson Quinn <jameson.qu...@gmail.com> > To: EM <election-methods@lists.electorama.com>
> Here's a toy model where the math is easy and you can get some interesting > results. > > -Voters are distributed evenly from [-1, 1] along the ideology dimension. > -Candidates are represented by an ordered pair (i,q) where i is an ideology > from -1 to 1 and q is a quality from 0 to 2. Such a one-dimensional ideology dimension grossly over-simplifies IMO.In reality, people do not line up along a simple one ideology dimension. Political scientists tend to oversimplify, beginning with Anthony Downs. The mathematics could take into account more than one issue position or dimension when using spatial geometry to model how close voters and candidates are to each other. It's on my to-do list to write up a far more logically coherent way of using spatial analysis of positions of voters and candidates that would essentially unify much of the field of voting behavior research -- although political scientists seem to enjoy carrying on the same debates endlessly rather than deriving new theory on what they agree on. Condensing reality down to one ideological dimension, even adding one quality dimension, grossly distorts the more complex picture of reality. A unidimensional model cannot even accurately model how three different persons, say candidates, stand on two different issues relative to each other or to voters. I think Downs basic approach makes sense only if his mathematics is repaired to respond to the multi-dimensional nature of the real world. -- 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 ---- Election-Methods mailing list - see http://electorama.com/em for list info