Re: [Election-Methods] Determining representativeness of multiwinner methods

[Steve Eppley]

Hi,

I don't find Terry's argument persuasive. (I used to believe it, years 
ago before I studied voting methods.  I thought it was important to have 
a "seat at the tables of power.")  The argument appears to assume 
significant debate occurs only within the legislature and that members 
of the legislature won't listen to expert witnesses and will listen only 
to each other.  I don't accept either assumption.  The argument that the 
public as a whole won't engage in robust debate is irrelevant, since 
robust debate takes place in many circles outside the legislature. 
(Internet email lists, for example.)

I don't think the "tackling" of issues, if that word merely means 
holding hearings on them and possibly drafting legislation, is nearly as 
important as the legislation that actually passes. (Which is what I 
meant in my previous message that the legislature's decisions are what 
matter, not its makeup.)

A counter-example to Terry's opinion is Kwame Mfuni, a former member of 
the US House of Representatives who chose to leave the House to become 
head of the NAACP because he felt he could accomplish more there than as 
a member of a minority (the Democrats) in the House.

Terry's "observation" that Vermont would have been better represented by 
a randomly selected legislature was not really an observation in the 
strict sense, it was only a guess. 

Don't misconstrue my argument as pro status quo.  I favor inducing 
competition to be around the voters' medians by using Condorcetian 
voting methods such as MAM--see my website at 
alumni.caltech.edu/~seppley--or a multiwinner variant of MAM, or the 
family of voting methods I call VPR (voting for a published ranking, 
which is easiest for the voters and can be fairly easy to tally).  The 
existing two party system is polarized, not (voter median) centrist, and 
comparing proportional representation only to the two party system is a 
false dichotomy.  If a majority of the people have the 
social/moral/empathic sense that would lead them to want society to 
collectively assist needy strangers (homeless, under-insured, jobless) 
then a competitive majoritarian voting method would tend to elect mostly 
candidates of that sort.  Conversely, if a majority do not have that 
social sense, no voting method will compensate for it.

If we can return to the point I was making, Kristopher's definition of 
representativeness is too narrow if it's the decisions of the 
legislature that matter. (Even if Terry is right, his argument is 
consistent with my point about decisions.)  Why not modify Kristopher's 
simulations to compare the decisions of the legislature instead of its 
makeup?

Going off on a tangent now, since Terry mentioned he was an elected 
member of a third party...  I've often heard it said that third parties 
have historically influenced the two main parties positively by raising 
major issues neither party was addressing, followed by the claim that 
thus third parties still serve a valuable purpose.  However, that 
history was during the "bad old days" before the two main parties opened 
their nominations to primary elections.  Nowadays, I reason, if a person 
who leans toward the platform of a third party can't win nomination in a 
primary election within one of the two main parties, s/he won't win the 
general election either, and s/he can raise major issues during the 
primary election.

Regards,
Steve
-------------------
Terry Bouricius wrote:
Steve,

I can speak first-hand about the reason to have a legislature that is as 
broadly diverse as the population, rather than made up of centrist 
majoritarians... (I served ten years as a third party member of the 
Vermont House of Representatives in the USA).

Society benefits from robust debate, and the consideration of ideas and 
perspectives beyond what is currently the majority view. The quality of 
decisions a legislature makes will be better if these alternate views are 
part of the in-legislature debate. The public as a whole does not engage 
in robust debate that may result in the evolution of current majority 
views (and our mass media certainly don't help), and new issues come up 
that were not issues during the election, so no majoritarian selection 
resulted from that election.

If a majority of residents in a society happen to be home-owners with 
health insurance, and decent jobs, would a legislature made up of 100% 
such people be more or less likely to tackle the issues of renters, 
without insurance and no jobs? And if they did tackle those issues, would 
they become sensitized to the perspective of those on the short end of the 
stick? When I served in the Vermont House, out of 150 members, there was 
only a single renter, and renters' rights were completely ignored (though 
30% of Vermonters are renters). I often observed that Vermont would have 
been better represented by any 150 people selected at random than by its 
elected "representatives" (of course Vermont uses FPTP winner-take-all 
elections).

That brings me to an interesting issue, which may be off-topic for this 
list..."sortition"...the selection of a legislative body by means of 
modern sampling methods that assure a fully representative body. There is 
an interesting history of the tension between sortition on one hand and 
election on the other (Athenian democracy used both), where sortition was 
seen as the more democratic method, with election being the lesser 
(because candidates with more money or fame had such an advantage over 
average citizens). It is the old question of whether representative 
democracy should be seen as "self-governance," or "consent of the 
governed."

Sorry if this is too off-topic.

Terry Bouricius


----- Original Message ----- 
From: "Steve Eppley" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Monday, June 23, 2008 11:20 PM
Subject: Re: [Election-Methods] Determining representativeness of 
multiwinner methods


Hi,

I prefer a definition of "representativeness" that differs from
Kristofer's.  To me, the more similar the *decisions* of a legislature
are to the decisions the people themselves would make collectively in a
well-functioning direct democracy, the more representative is the
legislature.

Given my definition, a non-proportional legislature comprised solely of
centrist majoritarian compromise candidates may be very representative,
since the people themselves would reach centrist compromises on the
issues in a well-functioning direct democracy.  It might be more
representative than a proportional legislature, since the proportional
legislator could match her constituents' favorite position on every
issue yet fail to match the way they would compromise.

Why should anyone care more about the legislature's proportionality than
about their decisions?

Regards,
Steve
----------------------------------------
Kristofer Munsterhjelm wrote:
  
Hello all,

(says the newcomer.)

I think I have found a metric for comparing multiwinner systems, at
least as these pertain to proportional representation, when all votes
are honest.

The advantage of the metric is that, if what it measures is desirable,
it gives an idea of how good the system performs - how representative
it is - and thus its best case performance. In contrast, criterion
failure shows how bad a system can get in the worst case.

The broad idea is this: The most proportional assembly is the one
which reflects the population on all issues. In other words, if a
fraction p of the population is of a certain position on a binary
opinion, it is better (ceteris paribus) for a council to have, of that
opinion, a fraction close to p than one far away from it.

Thus we could make a simulation. First, set that there are n binary
issues. Each of the voters then have an issue profile which consists
of n booleans. Set these randomly with different biases for each issue
(so that, for instance, on the first issue, 70% may hold the "true"
position, while on another, only 23% do).

Counting the proportion that hold the true-position for each issue
gives the popular issue profile. In general, the issue profile of a
certain subset takes the form of n numbers (for n issues), where each
number is equal to the proportion that holds the true-position for the
issue in question.

Then a perfectly representative assembly has an issue profile that is
equal to the issue profile of the people. So now we have a measure of
how well the assembly or council represents the people: the more its
issue profile differs from that of the people, the less representative
it is.

However, this presents a problem. How does one aggregate the
difference on each issue into a single score? Is a one-percent
difference on a single issue better than 1/n percent difference on all
issues? One way to solve this is to just settle on an aggregation
measure (like root-mean-square) and hope the results can be
generalized across; another is to use Pareto-domination as a measure
instead, in saying that councils produced by a method A is better than
councils produced by a method B to the extent that A-councils lie
strictly closer to the population profile than does B. That approach
can give no information on the cases where some issues are closer by
method A and some are closer by B (mutual nondomination).

Putting all of the pieces together, to figure out the scores, a
simulation would do something like this:
    - Generate issue vectors for all of the people, and get the
        popular issue profile.
    - Choose a subset of the people as candidates.
    - Generate ballots for each voter of all the candidates.
    - For a great number of random assemblies:
        - Get the issue profile of this assembly, and calculate
            the similarity measure for that with regards to
            the popular issue profile.
        - If the similarity measure is more similar or less
            similar than any random assembly we've seen so
            far, update the worst (respectively best)
            record.

    - For each multiwinner election system:
        - Feed the ballots into the system.
        - Get the issue profile of the elected assembly, and
            calculate the similarity measure for that with
            regards to the popular issue profile.
        - Normalize the similarity measure with regards to the
            worst and best random councils.
        - Add the normalized similarity measure to that system's
            running    total.

To be robust, it would do this a lot of times with various population
sizes, council sizes, and issue numbers (n). With a similarity
measure, 0 would be perfect (impossible most of the time), and 1 (or
infinity, depending on the measure) be the worst possible.

The only thing remaining is to find out how to generate ballots for
each voter. A reasonable assumption is that voters are going to prefer
the candidates who agree with them on many issues to those that agree
with them on a few. For binary issues, Hamming distance works: in the
simple model, voters rank (or rate) the candidates inversely of
Hamming distance.

--

I have made a program that does this. It is simple, does not use equal
ranks (randomizing preferences instead), but the results are 
interesting.

Worst of the lot are the majoritarian systems ported to multiwinner
systems. Those would, for a council of size k, just pick the k first
in the social order of the single-winner method. This result shouldn't
be surprising, because the straight port excludes minority opinion. Of
some curiosity, however, is that IRV does the best among those; maybe
it reflects IRV's origins as the multiwinner method STV? Or maybe
noise (as resulting from nonmonotonicity and the likes) bring it
closer to the results gained by just picking a random assembly.

Then come the vote-reweighted methods, like RRV. Vote-reweighted
methods can be generalized as: run a single-winner method, then
reweight those who voted for the winner, according to some function
that does not take the number of seats into account. Then run again,
and disregarding those that have already been elected, pick the next
member as the one who is closest to the top in the social ordering
output.

Best of all were the "proper" methods implemented: STV (with
Senatorial rules) and QLTD-PR, which uses Woodall's QLTD instead of
IRV as its basis: it adds fractional votes until someone gets above
the quota, then reweights the voters who contributed to that one,
basing the weighting on the candidate's surplus.

According to the RMSE scores:
    Majoritarian assemblies:
        Borda:         0.871528    *Plurality:       0.256192
        Antiplurality: 0.73616    Nauru-Borda:      0.599807
        IRV:           0.362097 Cardinal ratings: 0.894351

    Vote-reweighted assemblies:
        Borda:         0.376745    *Plurality:       0.260454
        Antiplurality: 0.401539    Nauru-Borda:      0.406815
        RRV (k = 1.0): 0.682116    RRV (k = 0.5):    0.644339

    Quota:
        *STV:          0.193959    *QLTD-PR:         0.121693
                    QLTD-PR (rated):  0.417813

    Other:
        Random Cands:  0.364437

    STV-QLTD Pareto dominance: QLTD: 236, STV: 237, nondomin: 674

    "Plurality" is the weighted positional system of {1, 0, 0....}
    applied to ranked ballots.

    (* marks those that are better than a random assembly, on
     average)

Some of the results may be due to artifacts in the voting pattern -
the simulator was a proof of concept, after all. I think that
Plurality benefits by that everyone votes sincerely, and that the
ballots are complete, for instance. Yet patterns emerge.

If anyone wants to experiment with the simulation program, it is here:
http://munsterhjelm.no/km/raw/pr_elect.zip . QLTD is called "Quota
Bucklin" there, as I sort of independently discovered it while trying
to make a quota-proportional form of Bucklin.

--

On a second thought, it shouldn't be so surprising that
vote-reweighted methods, in general, do worse than quota-based ones.
Consider the following situation:

    20: Left > Center > Right
    20: Right > Center > Left
     1: Center > Left = Right

Condorcet would pick Center in the single-winner case. In the
situation of an assembly of two, the reasonable choice (which CPO-STV
picks) would be Left and Right.

However, vote-reweighted methods based on Condorcet would have to
start off by picking Center, since all voters start off with equal
weights. After it has done so, there is not enough room on the
assembly to permit an even division of Left and Right, and thus either
Left or Right will be favored, assuming Center supports both sides
equally.

Vote-reweighted methods that aren't based on Condorcet may pick Left
and Right, but they can only do so if they would pick either Left or
Right in the single-winner case.
----
    
----
Election-Methods mailing list - see http://electorama.com/em for list info