[EM] Criterions for party-list PR systems

[Kristofer Munsterhjelm]

On 09/07/2015 11:44 AM, Vidar Wahlberg wrote:
> On Sun, Sep 06, 2015 at 04:31:13PM +0200, Kristofer Munsterhjelm wrote:
>> It is, of course, also possible that I simply haven't heard of the
>> concerns, rather than that they haven't been made. But as you say, it's
>> not as easily a measurable goal as voting criteria, and so I have to go
>> with what I know :-)
> 
> I must admit that I'm not very familiar with politics in Scotland nor
> Ireland. Like you, I too rely on my own experience as I don't know of
> any studies or papers on how party-list methods vs. candidate methods
> affect the political discussion. Looking at the US and UK elections,
> which arguably are examples of quite bad voting systems, it's my
> impression that there's far more focus on the candidates than you would
> typically see in Scandinavian countries. Obviously, correlation doesn't
> imply causation, so there could be entirely different reasons for this
> (and of course, I may have a bias that cause me to notice what
> strengthens my beliefs, while [involuntarily] overlooking facts that
> doesn't support by beliefs).

I agree about the US; I'm not as familiar with the UK. But the US is
untypical in other respects as well. What we'd really need is, as you
say, studies about which countries focus more on candidates' charisma
and personal attributes and which focus on more on issues and policies.
I suspect there are also confounding factors: I'd imagine less
democratic countries focus more on candidates as people. The ultimate
example of that would be "strong man"-type presidential systems.

The size of the constituency might also be of importance. I was reading
a weblog post about the direct mayoral election trials in Norway, and
the post said mentioned that, roughly translating, "Electoral research
indicates that the less populated the county is, the more the people
themselves matter" (http://bit.ly/1hQRm3S). If that is true and can be
generalized, then that would imply that Plurality would be more focused
on personal aspects than say, STV would, because the former only elects
a single winner per constituency and hence these have to be smaller.

>> The tricky part is finding out if the wiggle room provided inside the
>> DPC gives open party list STV enough rope by which to hang itself, so to
>> speak. We know it *can* trip up as a candidate method (as Woodall shows
>> in that it can fail both clone-in and clone-no-help); the question is
>> whether one can reach any of those failure cases from a party list
>> expansion.
> 
> Did you mean that it can fail both clone-no-harm and clone-no-help?
> Woodall claims multi-seat STV should meet the clone-in criteria (but
> presents no formal proof of this claim).

I misread. Yes, you're right; Woodall doesn't show that STV fails
clone-in, and he does show that it fails clone-no-help.

> What I fear with an expansion from party-list to STV is vote management.
> As shown in the paper from Woodall you linked to, adding clones can
> help/harm other candidates. Arguably Schulze STV solves some of this
> concern, but that system adds a fair amount of complexity.

Right. I don't mean that we should use STV as a party list method, but
that imagining doing so will go a long way in showing what kind of
criteria can be applied to ranked party list methods: if a candidate
multiwinner criterion makes sense after you force ballots to fit the
expansion, then the criterion makes sense for a party list method as
well. And if a criterion doesn't, it might do so after the ballots are
restricted to party list type (as was the case for clone-no-harm).

> And finally a slight digression, what I dislike with STV is that popular
> 2nd preferences can be excluded early on:
> 20 A>B>C>D
>  1 B>C>D>A
> 20 C>B>D>A
> 20 D>B>A>C

That's probably because it has an IRV-like core. The surplus rules act
as a kind of "hard stop" that prevents IRV's dynamics from violating the
Droop proportionality criterion, but STV is still IRV within those
constraints.

A similar effect could occur in your party list plus elimination method
(where you run party list and eliminate the weakest parties by first
preference until every party gets at least one seat) if there are
multiple very small parties. "Everybody's second choice" among those
small parties might get eliminated prematurely.

More generally, within the constraints, elimination methods will follow
their unconstrained logic. An IRV-based multiwinner method will act
mostly like IRV (picking the strongest wing), and something like "STV
but eliminate the Condorcet losers" will act mostly like single-winner
Condorcet (electing candidates closer to the general center; i.e. moving
the sweet spot that will get a candidate elected as close to the
over-all center as it can until it bumps up against the Droop constraint).

Neither of these is ideal, but to deal more properly with it, I think
you have to use more complex rules. Methods that don't directly
eliminate (e.g. my Bucklin method) will probably be somewhat better, and
methods that optimize for some condition or take all combinations into
account (Monroe or Schulze STV) will be better yet. But they are complex.

Well, non-fractional Monroe can be stated quite simply in this form:

1. Each voter has a satisfaction score for each candidate (his rating of
that candidate).
2. Each candidate can be assigned (linked to) either zero or v/s voters.
If v is not divisible by s, duplicate each ballot until it is. (For
party list: each party can be assigned kv/s voters, where k is an integer).
3. Assign voters to candidates so that the total satisfaction is maximized.
4. The candidates who are assigned more than zero voters win.

... but the problem is that it's both very hard find the true optimum
and to verify that it is indeed the optimum. It's also Range-like; it's
possible to make an MJ version, but it would be more complex. Finally,
it is (I think) quota-based and so would fail population-pair
monotonicity. Making it divisor-based would again (probably) require
greater complexity.

Making a simple well-behaved proportional method is *hard*.

I suspect that Webster/Sainte-Laguë is already maximally well-behaved
for its simplicity: if you want greater fairness, it's going to come at
the cost of it being more complex. But how much more, I don't know.

(I also suspect that perfect proportionality is going to be NP-hard for
most ranked and rated ballot systems. So if you need to go beyond a
certain level of quality, it'll always be worst-case very hard to find
out who won. But I don't have a formal proof of this. My suspicion is
based on that similar problems, like clustering, are NP-hard, and some
voting problems can be formulated as instances of these.)