[EM] Proportional Representation Systems I'd Support

[Kristofer Munsterhjelm]

Kathy Dopp wrote:
> Upon cursory reflection and in response to my strong opposition to any
> nonmonotonic method and to any method that fail to treat all voters'
> votes equally, the only proportional method I know I would support for
> legislative representation would be the party list system where
> candidates appear only on one list, where parties can cross-endorse
> another party's list instead of presenting their own list for any
> particular contest. But I don't know how fractional left-over vote
> shares are handled when this system fails to initially elect all the
> seats with the required vote share per seat.  Is that when two or more
> parties join forces to elect the rest of the seats and haggle over who
> fills them?
> 
> Are there any other proportional methods besides the party list system
> that are monotonic and treat all voters' votes equally (unlike IRV and
> STV where some voters' votes rankings are counted when it would matter
> and some are not)?

As far as I've understood it, what you'd like is a method that is:

- proportional (fair)
- monotone
- summable (so it can be audited)
and provides good results.

This is very difficult. The only method I know of that passes all the 
criteria is party list PR. STV only passes proportionality, while my 
experimental method is monotone and proportional but not summable.

Some methods that are only proportional under strategy can pass all of 
those criteria. SNTV is one: vote for a single candidate, and when you 
want to populate the council, pick the k with the greatest number of voters.
A party that fields too few candidates will be worse off because they 
could have got more, while on that fields too many spreads itself too 
thin and so loses all. Therefore, each will have a number of candidates 
proportional to their estimated support. However, that is really just 
proportional by party and so a complex type of party list PR, and it 
requires central coordination (by the parties, to be absolutely certain 
no prospective candidates would wander off, become independents, and 
draw away votes).

-

I think your more complex party list PR (with cross endorsement) could 
work while still passing all three criteria. It's certainly summable and 
proportional, so the only difficulty would be in making it monotone. 
Simply distributing excess turns it STV-like. Perhaps something similar 
to my divisor trick could be used, but I'm not sure how.

One simple method meeting all three criteria, after a fashion, would be 
a cumulative party list: each voter gives each party between one and ten 
points. Each ballot is normalized by dividing each rating by the sum of 
how many point the voter gave, so every ballot has the same power. Then 
simply sum them up.
Here, voters can support more than one party. The problem is that there 
isn't any contingency mechanism, so voting for a minor party may still 
waste your vote (because less of your vote goes to the other parties). 
It's only proportional according to the normalized vote counts.