[EM] Weighted voting systems for proportional representation

[Kristofer Munsterhjelm]

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.