On Wed, Aug 3, 2011 at 5:22 AM, Jameson Quinn <[email protected]>wrote:
> > > 2011/8/3 Juho Laatu <[email protected]> > >> I noticed that there was a lot of activity on the multi-winner side. >> Earlier I have even complained about the lack of interest in multi-winner >> methods. Now there are still some interesting but unread mails in my inbox. >> >> Multi-winner methods are, if possible, even more complicated than >> single-winner methods. Maybe one reason behind the record is that there are >> still so many uncovered (in this word's regular non-EM English meaning) >> candidates to cover. >> >> Juho >> > > OK, on the theme of simple multi-winner systems I haven't seen described > before, here's a simple Maximal (that is, non-sequential) Bucklin PR, MBPR. > Now that the sequential bucklin PR methods have been described, it's the > obvious next step: > > Collect ratings ballots. Allow anyone to nominate a slate. Choose the > nominated slate which allows the highest cutoff to assign every candidate at > least a Droop quota of approvals. Break the tie by finding the one which > allows the highest quota of approvals per candidate (the slate whose members > each satisfies the most separate voters). If there are still ties > (basically, because you've reached the Hare quota, perfect representation, > aside from bullet-vote write-ins) remove the approvals you've used, and find > the maximum quota per candidate again (that is, look to for the slate whose > members each "double satisfies" the most separate voters). > > Obviously, this needs to use the contest method to beat its NP-complete > step. But all the rest of the steps are computationally tractable. Except > for the NP-completeness, this or some minor variation thereof (diddling with > the order of the tiebreakers between threshold, quota, and double-approved > quota) seems like the optimal Bucklin method. I'd even go so far as to say > that it seems so natural and "right" to me that, if it weren't NP-complete, > I'd consider using it as a metric for other systems, graphing them on how > well they do on average on the various tiebreakers. > Sounds like a good system to me. Keep bringing it up so I'll remember to keep thinking about it. :) Seems similar to Monroe in some ways... Is there any sense lowering the cutoff for the tie-breaker phase? Maybe if you can't find any slates that "double satisfy" all the voters with the original cutoff, you could with a lower cutoff. Just thinking out loud... Andy
---- Election-Methods mailing list - see http://electorama.com/em for list info
