[EM] Level of proportionality for two-seat PR methods

[Kristofer Munsterhjelm]

On 2026-06-13 09:05, Toby Pereira wrote:
> More interesting work. Like you I'm surprised by the position of random 
> ballots. Is it not the case that if you pick two random numbers between 
> 0 and 1, the expected value of the lower number is 1/3 and the higher 
> number 2/3? Not 1/4 and 3/4. And is that not essentially the same question?

Hmm, yes, I'm not sure what's going on here. I thought that perhaps the 
outcome is different because each voter ranks candidates in order of 
distance, so that the optimal candidates are related to what minimizes 
the sum of distances, but the quick and dirty Python script I just wrote 
seems to show that 1/3, 2/3 is also what minimizes the expected sum of 
distances between a random voter on a normal and the closest candidate.

I'll have to look into it further at some point :-)

-km