[EM] Thermodynamics

[Kristofer Munsterhjelm]

On 05.06.2022 19:16, Carl Schroedl wrote:
> As a software guy, the connection I make is to something I have wondered
> for a while -- whether it is useful to study social choice functions as
> lossy compression algorithms. I haven't thought it through, but it could
> be interesting to see if the rate-distortion branch of information
> theory would apply.

If you're trying to design a method that has the best possible VSE for a
ranked voting method, then it may be possible to use ideas from vector
quantization. In a spatial model, the voters rank the candidates
according to proximity, and then the method finds the winner that's
closest to the voters using only this information. So it's trying to
find a vector (n-dimensional point) that's closest, in an Euclidean
sense, to the distribution of the voters... though unlike ordinary VQ,
it doesn't know the actual distances, only their ranking.

Similarly, I'd say quota-based proportional representation is like
clustering. Monroe's method is the most obvious clustering-like PR
method: you assign each candidate a voter, so that each candidate has
the same number of voters, and so that the total voter-candidate
distance is minimized. (One possible objection to Monroe is that it
doesn't care about what the voter thinks about the composition of the
rest of the assembly, just his preferred candidate.)

That's for honest voters, though. With strategic voting, the
"compression method" (clustering method) becomes partly adversarial:
keep the outcome from degrading too much if some fraction of the votes
is arbitrarily altered.

-km