[EM] Exact spatial model probabilities?

[Daniel Carrera]

On Wed, Jan 26, 2022 at 1:30 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> I should probably give more of an explanation for the choice of the atomic
> electo-potential, i.e. the scalar potential function V(r) for one voter
> located at R:
>
> V(r)=||r-R||
>
> The force=-grad V(r) represents the influence of the voter pushing or
> pulling in one direction or another. The true winner should be at a point
> where the resultant force of the entire electorate is balanced at as close
> to zero as possible.
>
> So what is the force of one voter under this choice of potential V(r)?
>
> It is -grad V(r) anchored at the voter position R.
>


I don't think that it really makes sense for a voter's force to follow a
1/r^2 law. That would mean that two candidates that are both extremely
close to you can have vastly different forces while two highly dissimilar
candidates that are far from you get nearly the same force. That doesn't
seem like a realistic model. If I am a Bernie Sanders voter I would be
mostly indifferent if I got AOC instead, but I would have a strong view
between a center-right and a far-right party.

It might be more accurate to see the force from a voter as linear with
distance --- every voter holds an elastic band that follows Hooke's law.
This can still be expressed in the language of potentials if that's useful.

Cheers,
-- 
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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