# [EM] Proportional Representation in CIVS

Kristofer Munsterhjelm km_elmet at t-online.de
Tue Oct 22 13:57:06 PDT 2013

```On 10/21/2013 05:17 AM, Dick Burkhart wrote:
> The problem with all methods that use the Droop formula or something similar
> is that it is not actually clear if any these methods are truly
> proportional. In fact, what would true proportionality actually mean?

To methods passing DPC, a certain minimum measure of proportionality is
very simply defined. The criterion says that "if more than q Droop
quotas' worth of voters vote the same k candidates ahead of everybody
else (but not necessarily in the same order), then min(q, k) of these
should be on the council".

Comparable to mutual majority for single-winner methods, it might not be
an end-all measure of proportionality, but it provides certain
guarantees. A single-winner method that passes mutual majority may also
be bad (like IRV) or good (like Condorcet), but if I had no other
information, I would take a method that passes it over a method that
fails it.

In that respect, it is again like single-winner criteria. They don't
dictate what the method should do under all circumstances, but they say
that "we at least want this to be true", or "when you do X, undesired
effect Y shouldn't happen" (depending on the criterion type).

> If the groups to be proportionally represented are predefined, you must
> decide what constitutes a vote for them. Not so easy, if either a candidate
> or a voter has divided loyalties.

This is indeed a problem, and it's most readily apparent when making
"Condorcet-ish party list methods". For party list, how much should a
second preference count against a first one? I tried to make Condorcet
party list methods (CPO-SL and an unnamed one that was rather kludgy),
but I'm not entirely satisfied with them. They're still better than
Plurality-based party list, though.

> If the groups are not predefined, then the groups themselves must be
> determined by a pattern recognition technique. That is, all ballots in a
> group must be similar in some sense, but it is not clear a' priori how to
> construct the best definition of similar ballots. For example, two ballots
> may top rank a candidate identified with one group, but the second ranked
> candidates could be identified with different groups, and third ranked
> candidates could be even more different, while the fourth ranked might go
> back to the original group, etc.
>
> In addition, it is typical that different groups will overlap. For example,
> some voters will be both in a "labor" group and an "environmental" group,
> and their ballots will generally reflect this. It gets even more complicate
> when you consider that candidates themselves will have similar overlapping
> interests, so if a voter gives a high ranking to a candidate who considers
> himself / herself both a "labor" person and an "environmental" person, how
> do you classify that ballot?

Well, say you have some voters voting so that, from first rank down:

2+e DQs vote for {labor} > {environmental} (i.e. rank all labor
candidates in some order, then all environmental ones right after)
2+e DQs vote for {labor, environmental} (i.e. intermixes them evenly)
2+e DQs vote for {environmental} > {labor},

where e is an epsilon, and "2+e DQs" mean 2+e Droop quotas' worth. Then
a method that passes the Droop proportionality criterion recognizes the
following:

more than 6 Droop quotas voted for {labor, environmental} seen as a
whole. So 6 seats should go to that supergroup.
Of that supergroup, 2 preferred labor to environmental, 2 preferred
environmental to labor, and 2 were evenly split.

Thus that supergroup should get at least 2 labor candidates and at least
2 environmental ones, and most methods would give 3 labor and 3
environmental ones. Which labor candidates or which environmental ones
depends on the method in question - for instance, STV might be a lot
more IRVish than Schulze STV here, and might not elect a compromise
candidate between labor and environmental.

> Even when you've identified good groupings, you are not done. There be other
> groupings which are better in some sense, or almost as good. Then you must
> match the candidates to the groups in the "best" way, whatever that might
> mean, given that you can't split candidates and given the divided loyalties
> of some candidates.

Not entirely done, no, as the ambiguity above shows. Still, the DPC says
"you can't go worse than this", and it's seems intuitively fair.

Though just to be precise, there may be situations where you'd like to
fail the DPC. But then you would have a better idea of proportionality
to put instead. Say you're making a Sainte-Laguë based method. If it
reduces to Sainte-Laguë/Webster party list when the voters plump only
for candidates of a certain party, then that method will fail the DPC in
certain (rare) cases -- but it could be better than DPC methods for the
same reason highest averages list methods are better than least
remainders ones.

> That's why I've developed a "Clustering Algorithm for Proportional
> Representation" - to attempt some reasonable answers to such questions, and
> to gain more insight that is given by relatively opaque methods like Single
> Transferable Vote.

I imagine you've seen Monroe's method, then. I also made a clustering
method based on Kemeny, but its runtime was prohibitive. I *think* it's
possible to make a clustering method based on Young's method - something
to the effect of "cluster the ballots so that, ignoring as few voters as
possible, each cluster elects a different CW". I seem to recall it being
possible to phrase that as a single integer program and thus the method
could be run for small councils instead of blowing up almost immediately
(as the Kemeny one did).

Also of interest might be my multiwinner proportionality vs majoritarian
satisfaction simulations. They're based on generating a hidden yes/no
opinion space, assigning opinions to every hypothetical voter, and then
the voters rank candidates in order that they agree. One can then use
proportionality measures like the Loosemore-Hanby index or the
Sainte-Laguë index on the opinion space distribution in the council that
results (when the ballots are fed through some given method) in
comparison to the opinion space distribution of the voters themselves.
It is similar to what one does when measuring party list PR
disproportionality, only on opinions the method never directly sees.

Finally, speaking of "what is proportionality, anyway?", I wrote a bit