[EM] Improved IRV

[Richard Lung]

Thankyou for interesting responses. I did wonder what these "multi-winner contests" were (in plain English, as well, as if I were an ordinary voter, without acronyms. I admit I use them myself, but am old and slow with others.) This is the situation we are in with election methods, recognised by brand names.
If I may say so, the most obvious theoretical reason, against pairing contests, I take it, KM means by Condorcet-based methods, has been over-looked. The theoretical objection was made over two centuries ago by Pierre-Simon Laplace, once regarded as one of the half-dozen greatest mathematicians in history. Namely, that Borda was to be prefered to Condorcet, because preference votes are not of equal importance. It is true that Borda is only an assumed weighting of rank, but at least it recognises the need. (JB Gregory supplied real weighting of rank.)
That Laplace law was reinforced, in the 1940s by SS Stevens on scales of measurement. Borda supplies the necessary interval scale (assumed)
 Gregory improves on that by supplying a real interval scale. 

The only Condorcet-augmented STV, I vaguely remember, is Sequential STV, by Dr David Hill. I think it was meant to tie-up a loose end but was admittedly non-monotonic.
This problem was solved rather by giving STV a rational exclusion count, as well as a rational election count -- Binomial STV, which KM found to be monotonic.

Regards,
Richard Lung.    




On 25 Mar 2023, at 10:07 pm, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:

> 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
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