[EM] Improved IRV

[Kristofer Munsterhjelm]

On 25.03.2023 21:34, Andrew C. Myers wrote:
> Richard Lung writes:
>>
>> Personally, I doubt whether pairwise contests are really suitable for 
>> more than single member contests (which are monopolistic not 
>> democratic enough, despite politicians contentions). My limited 
>> experience is that, in single member contests, weighted Condorcet and 
>> Borda methods are in agreement, as rational counts of quite marginal 
>> contests, compared to mere elimination methods, like Suppementary 
>> Vote, FPTP, IRV/AV, which are only ordinal scale measures (of more or 
>> less), not more accurate rational representations of data.
>>
> My rather extensive experience with CIVS (36000+ elections) suggests 
> that Condorcet methods work just fine for multi winner contests. The 
> system is used routinely for that purpose by a number of organizations 
> whose names you would recognize.

There's no obvious theoretical reason why Condorcet-based methods can't 
be used for multiwinner either. As Schulze STV and CPO STV show (and I 
imagine the CIVS multiwinner method too), multiwinner methods that make 
each council assigment (choice of candidates to seats) into a virtual 
candidate can pass Droop proportionality by using an appropriate 
function for comparing these assignments.

It's even possible to make Condorcet methods that pass Droop and 
single-winner Condorcet without having to deal with the combinatorial 
explosion of (n choose k)^2 virtual candidates. STV with (e.g.) Ranked 
Pairs loser elimination is a simple example.

I think, though I'm not sure, that it's possible to make a Webster-type 
Condorcet multiwinner method as well. I sketched one a long time ago, 
although I'm not sure it's correct.

(An interesting question would be: what's the simplest pairwise 
comparison function that ensures Droop proportionality?)

-km