[EM] Proportional Representation Systems I'd Support

Kristofer Munsterhjelm km-elmet at broadpark.no
Mon Mar 22 14:24:25 PDT 2010

```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.

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