[EM] Retraction--Approval Voting and Classical Mechanics
Alex Small
asmall at physics.ucsb.edu
Wed Sep 10 17:11:04 PDT 2003
A few weeks ago I proposed a model of candidates maneuvering in issue
space. I thought I saw a connection between candidates in issue space and
the motion of objects subject to nonlinear forces in classical physics.
Specifically, I wrote the following:
> The important result is that force on candidate i is the gradient of a
> scalar function, and that scalar function depends only on the positions
> of i and the other candidates. At this point we can bring in all sorts
> of advanced machinery from classical mechanics to analyze this.
This is wrong! Why?
In a nutshell, the "force" on each candidate is indeed the gradient of a
scalar function, but it's a different scalar function for each candidate.
The machinery of classical mechanics (or at least the machinery that I'm
familiar with) can only be brought to bear if the scalar function that
gives the force is the same for every object in the system. Depending on
the formulation that function may be the Lagrangian, the Hamiltonian, or
the action (S, the solution of the Hamilton-Jacobi equation).
If somebody wants I can go through the messy math to show my error, but
for now I'd rather not.
Alex
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