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

[Jameson Quinn]

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

> On Sun, Nov 6, 2011 at 5:36 PM, Jameson Quinn <jameson.quinn at gmail.com>
> wrote:
> > 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.
>
> Are you saying the Condorcet winner is not necessarily the utility winner?
>
> Exactly. For two candidates, there is some probability less than 1/6 that
the pairwise winner is not the utility winner. That probability would drop
further as you added candidates and went from "pairwise" to "Condorcet". My
intuition from playing with this toy model (that is, staring out the window
at the nice conical volcanoes that inspired it) is also that adding
ideological dimensions to the model and using a more-realistic voter
distribution (normal, not flat) would increase that probability marginally,
but I'd wager that it would stay under 1/3.



> > 3. It is therefore reasonable to hope for a voting system that tends to
> > elect centrists, but slightly less so than a Condorcet system.
>
> Why would utility be considered more important than centrist?  Or would it?
>
> Utility is *the* goal, almost tautologically. I mean yeah, there's plenty
of ways you could criticize the model, or even the idea that the votes have
anything at all to do with the utility that the voters will gain from a
given candidate winning; but until someone comes up with something better,
for democracy at least, utility is the best paradigm we have.

Jameson
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