[EM] Survey of Multiwinner Methods

[Kristofer Munsterhjelm]

On 01/08/2013 09:24 AM, Greg Nisbet wrote:
> There's some definite motivation for writing the list of criteria to
> exclude parties, districts, and relying on candidates making decisions.
> These sorts of mechanisms are not always available (for instance,
> picking pizza toppings or locations or something of that nature). That's
> not to say that these methods are never useful or not "competitive" with
> party-less, district-less, candidate-decision-less methods in some sense
> ... it's just harder to compare their merits in some sort of "universal"
> sense without considering very specific factors about the community
> associated with the election. In that sense, limiting focus to methods
> that don't impose these sorts of additional structure or requirements on
> the candidates or voters helps to simplify things rather dramatically.
>
> I'd like to point out that this still leads plenty of room for
> creativity / is perhaps not restrictive enough a requirement to really
> create a fair comparison.
>
> For instance consider a form of Cumulative Voting where each voter
> receives n votes to use in each of m rounds with the results being
> published at each intermediate stage and voters each allowed to cast n
> votes again while knowing a little bit more about the outcome.
>
> How would one compare this method to STV or List PR or districted
> [Favorite Single-Winner Method Here]? It's hard to say and may depend
> very much on what sort of assumptions you make about people and their
> behavior.

Few methods incorporate parties or candidate decisions into their own 
logic. The mechanism that is STV, for instance, works perfectly well on 
an election of 8191 winners from 32767 candidates. The problem, of 
course, is that no voter would want to rank 32767 candidates.

The exceptions I can think of are party list and MMP (requires parties, 
but these may be nonpartisan "county lists"), and Asset and 
candidate-withdrawal methods (require candidates to do something).

I guess you could say that some methods have soft limits: unless you 
turn the solar system into a huge computer, you're not going to run 
CPO-STV with 32767 candidates (in the worst case). There's no hard limit 
that says you can't run CPO-STV with that many candidates - it just gets 
highly impractical.

But most of the problems with running on huge numbers of candidates 
relate to the voters themselves. For example, your Cumulative Voting 
system would have problems with huge numbers of candidates simply 
because the voters' attention would be spread too thin to judge how to 
juggle the m votes between n rounds with m and/or n large. The voting 
methods are very general, but to apply them right, one has to make the 
actual voting manageable, which is where districting (simplification by 
area of real space) or parties (simplification by area of opinion-space) 
would enter the picture.