[EM] Ideas for another proportionality measure

[Kristofer Munsterhjelm]

On 2026-05-19 00:34, Etjon Basha wrote:
> Hi Kristofer and all,
> 
> Perhaps not super practical, but the Monte Carlo random vote appeals to 
> me: in your scenario above, run it 100 times with two random voters 
> voting each time in sequence. So, 81% of the outcomes would be A and B, 
> 9% E and D, and the rest some mix of A and E. Sum over all outcomes and 
> see the top two? Would this be the platonic proportional benchmark, that 
> doesn't require us to splice the voters into n dimensions of 
> proportionality?

I imagine that would have a center squeeze problem. Consider 
single-winner with LCR:

40: L>C>R
30: R>C>L
20: C>L>R

Random ballot picks L and R more often than it picks C, but C is the 
closest to the median voter.

This kind of "low-pass" makes proportional representation with fewer 
seats difficult, because you want both factional representation and 
general support.

I suspect that a multiwinner generalization of median voter would have 
to take strategy or incursion resistance into account somehow. Ryan may 
be pointing at something similar in his post when he says that a Droop 
quota can force a certain winner to win in SNTV; and incursion 
resistance would be something like the single-winner median voter 
theorem where in a majority election, if the winner is not near the 
median voter, someone can place themselves closer and win.

I'm just not sure how to do so in a platonic sense.

-km