[EM] Weighted voting systems for proportional representation

[mrouse1 at mrouse.com]

> 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 :-)
>
> As a single-winner method, it reduces to Range or Borda respectively.
>
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If I am reading it correctly, it sounds very similar.  It's a pretty
simple way to give most voters their preferred candidate in the
legislature -- relatively fewer people would be without any candidate to
represent them.

The main difference is that it doesn't distinguish between weak and strong
winners, while the weighted version would give different candidates
different weights (or voting strengths). Most people would probably want
to either spread "extra" votes from strong winners to like-minded people
(parties), or give strong winners proportionally greater power (weighted
or proxy voting).


(In the weighted version, every time a candidate in the winning slate was
the most highly rated on a ballot, he or she would get an extra vote in
the legislature. If there were a tie, the vote would be split
appropriately.)