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

[Jameson Quinn]

2011/8/8 Andy Jennings <elections at jenningsstory.com>

>
>
> 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...
>


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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