[EM] Record activity on the EM list?

[Jameson Quinn]

2011/8/3 Juho Laatu <juho4880 at yahoo.co.uk>

> 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.
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