[EM] STV question (was: re: Hare clustering)

[Kristofer Munsterhjelm]

On 11.02.2022 16:09, Colin Champion wrote:
> I don't think this quite works. Suppose that there are 6 seats and that
> 2/3 of the voters are concentrated at a point X with 1/3 at Y. The best
> result is to elect 4 candidates at X and 2 at Y, but neither my metric
> nor yours cares what the balance is between candidates elected at the
> two points (assuming that 'their representatives' means 'their closest
> representatives').
> 
> Maybe it's not so easy.

You can of course make it a hard constraint. That's what Monroe's method
does:

Let f(v, c) be some function that produces a score for voter v's
preference for candidate c, where greater is better.

Assign (possibly fractional) voters to candidates so that the number of
voters assigned to each candidate is equal, the number of candidates
with some voters assigned is equal to the number of seats, and so that
the sum of f for each voter and his assigned candidate is maximized.

Condorcet variants should be possible, e.g. let X_1 and X_2 be some set
of candidates with cardinality s, then X_1>X_2 is equal to the number of
voters who strictly prefer the assignment in X_1 to the one in X_2.

Trying to engineer the optimization function so that it achieves PR
without needing explicit constraints has usually been the domain of
cardinal advocates because ordinal ballots don't provide any strength of
preference information. See e.g. https://rangevoting.org/QualityMulti.html.

-km