2011/8/8 Andy Jennings <[email protected]> > > > 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... >
Yes, tiebreakers with a different cutoff (either lower, to find "double-satisfying" slates, or higher, to find the most-representative slate even if none reaches the Droop quota), would work. JQ > > Andy >
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