[EM] Weighted voting systems for proportional representation

[Kathy Dopp]

> From: Kristofer Munsterhjelm <km_elmet at lavabit.com>
> To: mrouse1 at mrouse.com
> Cc: EM <election-methods at lists.electorama.com>
> Subject: Re: [EM] Weighted voting systems for proportional
>        representation
>
> mrouse1 at mrouse.com wrote:
>> I emailed Forest about using weighted voting systems (ones where
>> candidates, rather than parties, have different voting power in the
>> legislature), and he suggested posting it to the group for discussion.
>>
>>
>> The following method could be used with Approval, Range, and Borda ballots.
>>
>> 1.  Determine the size of legislature you want.
>>
>> 2.  Have each candidate list all of the other candidates in order of
>> preference.
>>
>> 3.  Looking at every possible slate of candidates in turn, add an amount
>> equal to the highest scoring candidate on each ballot to that slate?s
>> score.
>
> Although it might only be slightly related to your system, this makes me
> wonder if the following very simple combinatorial method is any good:
>
> - Input ballots are Range or Borda.
>
> - Any given slate has a score equal to the sum of, over all ballots, the
> highest rated candidate on that ballot that is also in the given slate.
>
> - The slate with the highest score wins.
>
> - Tiebreaks are leximax (sum of, over all ballots, the second highest
> rated candidate, etc).
>
> I don't think that passes DPC (since Borda doesn't pass Majority), but
> it passes the weaker "force proportionality" criterion (in that an 1/n
> faction can, by strategy, force their representative to be the one they
> want). So it is at least better than SNTV, except for the whole bit
> about not being summable :-)

It *is* a summable method because it would simply require reporting
and summing the sum from each precinct for every ballot's (1) 1st
choice candidate, (2) 2nd choice candidate, and so forth.

On first glance, I like this method, including the leximax tie-breaker
for possible slates which garner the same number of 1st choice votes
(I assume this can be continued if some slates garner the same # of
1st and 2nd choice votes to examine the 3rd choice candidates) which
seems very fair.

Looks like it is unnecessary to have the candidates list all the other
candidates in their preference order because the voters decide on
which slate of candidates wins out of all the possible slates.  This
seems like a fairly simple, equitable proportional voting system that
can use several ballot styles (Borda, range, or approval) as input.  I
like it - although I've not examined it in depth in a spreadsheet yet.

>
> As a single-winner method, it reduces to Range or Borda respectively.
>

Kathy Dopp
http://electionmathematics.org
Town of Colonie, NY 12304
"One of the best ways to keep any conversation civil is to support the
discussion with true facts."

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

View some of my research on my SSRN Author page:
http://ssrn.com/author=1451051