[EM] Maximal Bucklin PR (was: Record activity on the EM list?)

Andy Jennings elections at jenningsstory.com
Mon Aug 8 11:37:34 PDT 2011

```On Wed, Aug 3, 2011 at 5:22 AM, Jameson Quinn <jameson.quinn at gmail.com>wrote:

>
>
> 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.
>

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
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