[EM] Exact spatial model probabilities?

[Forest Simmons]

El jue., 27 de ene. de 2022 1:44 a. m., Daniel Carrera <dcarrera at gmail.com>
escribió:

>
>
> 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||
>>
>
You must have read this as V(r)=1/||r-R||, which would yield the inverse
square law of force,

But the V(r) actually written gives a force of -grad||r-R||=(R-r)/||R-r|| a
unit force pointed towards the voter position. Each voter exerts the same
amount influence, but different direction depending on the position of the
voter.


>> 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.
>
Hook's law gives more influence to the distant voter.

Think about voters distributed along a straight line ... Hook's law would
choose the mean voter candidate instead of the median. The extreme voters
would have undue influence.

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