[EM] [CES #3320] Re: connection between multiwinner voting systems & districting problems

[Jameson Quinn]

2011/7/28 Andy Jennings <elections at jenningsstory.com>

> On Thu, Jul 28, 2011 at 6:50 AM, Warren Smith wrote:
>
>> To draw districts using a multiwinner voting system:
>> Let there be V people, whose coordinates are known.
>> Let the "candidates" be the same set as the people (V candidates).
>> Each voter "votes" by ranking the "candidates" in order of increasing
>> distance
>> away from her, or somehow scoring them (in a score-based voting
>> system) using some decreasing function of distance.   (Actually, all
>> these votes are fake in the
>> sense that they are automatically generated from the coordinates; no
>> humans actually vote.)  We then "elect" W winners.
>> These winners will be the centers of the districts.  [Once the
>> district centers are selected there is a known polytime algorithm for
>> finding the best assignment of the people to the districts such that
>> the sum of the distances (or squared distances) to the district
>> centers is minimized subject to the equipopulousness constraint.]
>>
>
> Good idea.  Hadn't thought of it that way before.
>
>
>> We can now attempt to evaluate various multiwinner voting systems by
>> asking how well they would perform for districting purposes.
>>
>> Consider, e.g, Andy Jennings' "greedy algorithm"
>> which selects the candidate whose Tth highest score is greatest (where
>> T is the district target population) and removes the T voters who
>> scored him with the T highest scores, as "district #1" -- then
>> continues on with the remaining voters.
>>   It would work pretty well at first, removing chunks of people in
>> dense cities, each chunk having population equal to a district target
>> population.  However, as it proceeded, eventually your country would
>> start to look like swiss cheese, with many removed "holes."
>> The late districts Jennings produced, would necessarily be quite bad,
>> large,
>> containing a lot of scattered people, and with a lot of holes in the
>> middle of those districts.
>>
>
> Interestingly enough, people in Arizona wanted it that way at one point.
>  Some people think Arizona's 1st district (
> http://en.wikipedia.org/wiki/Arizona's_1st_congressional_district) is the
> way it is because of gerrymandering, but I'm pretty sure it was a
> non-partisan committee who designed it that way so rural interests could be
> combined and have their own representative.
>
> Then again, it was the district that elected Rick Renzi, accused of being
> one of the most corrupt congressmen at the time.  Does this reflect
> negatively on the swiss cheese idea?  In any case, I agree that most people
> would reject swiss cheese districts.
>
>
Note that some form of swiss cheese might actually be optimal with a metric
like "minimize people's average square root of distance to center". I'm not
saying it's what people want, I'm just pointing out that it is has some
arguably optimal property.

JQ
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