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

[Jameson Quinn]

The point of this model is not to accurately reflect reality, but to
demonstrate how easy it is to get some simple, yet perhaps
counterintuitive, results. That's why I repeatedly called the model a "toy".

In this case, what I demonstrated in my previous message almost certainly
generalizes to more-realistic numbers of dimensions and distributions of
voters. To wit:

1. The pairwise winner is not necessarily the utility winner, even for
honest voters in a smooth distribution with symmetrically-shaped preference
functions.
2. On the whole, the more-centrist candidate in any pair is more likely to
be both the pairwise winner and the pairwise winner. If, however, the
centrist is only one of those two things but not both, the chances are that
they win pairwise but not in utility.
3. It is therefore reasonable to hope for a voting system that tends to
elect centrists, but slightly less so than a Condorcet system.

I absolutely encourage and support anyone else who wants to make
more-realistic models. I think that to improve our understanding, both
simplistic "toys" and complex models can help.

Jameson

2011/11/6 Kathy Dopp <kathy.dopp at gmail.com>

> > From: Jameson Quinn <jameson.quinn at gmail.com>
> > To: EM <election-methods at 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
>
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