[EM] Why proportional elections - Power arguments needed (Czech green party)

[Peter Zbornik]

On Wed, May 19, 2010 at 9:43 PM, Kristofer Munsterhjelm <
km-elmet at broadpark.no> wrote:

> Peter Zbornik wrote:
>
>> Dear Kristoffer, dear readers,
>>  Kristofer, you wrote below: "A minor opinion within the party might need
>> time to grow, and might in the end turn out to be significant, but using a
>> winner-takes-it-all method quashes such minority opinions before they get
>> the chance."
>>  Thanks, yes I have used this line of argument a lot (we actually have a
>> global charter of the greens, according to which the greens are obliged to
>> put the same principles into practice in thei organizations as they work for
>> in society).
>> The problem is, that this argument does not "stick", it is simply not
>> sexy.
>>  Would it be possible to measure the "utility" or "happiness" among the
>> voters in the party compared to different election methods. I saw you
>> Kristofer did some work on this but I didn't understand it, I guess I lack
>> the preliminaries.
>>  I guess the notion of "Bayesian regret" or something similar could be
>> used to argue that proportional elections are better than block-voting, but
>> I have no idea of how to explain this, as I don't know the subject at all
>> (pareto optimal social allocations, or whatever).
>>
>
> Yes, I made a voting simulator using a binary issue model to determine
> proportionality. Very simply put, each voter and candidate has a number of
> bits specifying whether the voter/candidate in question takes the "yes" or
> the "no" position on each issue, voters prefer candidates with similar
> opinions, and proportionality is determined by comparing the fraction of
> "yes" for each opinion when considering the elected council members alone
> and the population in general - the closer, the better.
>
> However, that metric is only of interest if you already think
> proportionality is a good thing. By using the metric, I have found that some
> methods are more proportional than others; but I have also (later) found
> that there often is a tradeoff. Some methods are better than others on both
> proportionality and on majoritarian satisfaction (by metrics such as
> Bayesian regret), but beyond this, a method that is more proportional is
> also worse from a majoritarian point of view.
>
> This should not come as a surprise in hindsight. Proportionality forms a
> constraint, and majoritarian satisfaction another. While proportionality
> seeks to set the council so that any given group is well represented,
> majority satisfaction seeks to set it so that the majority of society, as
> one bloc, has its opinions represented. Giving a minority a voice leaves
> less for the majority, and there is your tradeoff.
>
> I may have given the link before, but I think it's a good graph showing
> this tradeoff for a council of two candidates:
> http://munsterhjelm.no/km/elections/multiwinner_tradeoffs/
>
> Scroll down a little to see the results graph.

Yes, your example is cool and gives food for thought.
However some explanations might help.
What is the Social optimum Pareto front? How do you calculate it? In what
publication is "Social optimum Pareto front"
On the page above, you write "Detailed data: election methods scores (Pareto
front)" -What is the difference between the election methods scores and the
Pareto front election data?
What is normalized Bayesian regret for ranked list, how do you calculate it?
Could you please give a simple example?


>
>  It seems intuitive that economic tools could be used (I know almost no
>> economics), since ranked ballot elections simply are explicitly stated
>> preference orderings.
>>  I guess that voting and elections, could be indeed one of the best
>> imaginable real-world examples, where preference orderings of the actors
>> actually are known, and thus all of the machinery of economic equilibria and
>> social welfare functions could be applied (like the Bernoulli-Nash social
>> welfare function).
>>
>
>  Game theory can be applied to single-winner methods, and has been with
> concepts like the uncovered set, minimal covering set, independence of
> Pareto-dominated alternatives and so on. Game theory can't really be applied
> to multiwinner methods because much less is known about multiplayer games.
> Further confounding the issue is the fact that voting is not rational in an
> economic sense; unless in a very small committee, any given voter has next
> to no chance of actually altering the outcome.

I guess this is correct if we analyse the decision between voting and not
voting for a "rational economic man".
The situation is different, when we assume that a person will vote with a
ranked ballot (like in the green party council elections or the elections in
any organization).
Then we get a "clean" economic problem.
I cannot think of a simpler and more important example in real life, where
the preference orderings of the actors are required to be explicitly stated.

>


> There have been attempts, though, including on this list (cabal equilibria,
> trembling hand equilibria, etc).
>
>  In the long run, proportional councils may also have benefits that can't
> be easily gleaned from game theory. For instance, the members of a diverse
> assembly may keep each other in check (and thus be less likely to be
> corrupt), drift less (for the same reason), and be less prone to groupthink
> (again for the same reason).

 These involve the broader purpose of an assembly as a discovery mechanism
> and executive, and could possibly be improved further by the use of advanced
> mechanisms of which we don't yet know.


>
>  I am personally interested in the possiblity of measuring utility, is
>> there some (preferably short) literature on social welfare, utility and
>> voting theory for proportional elections (I know some undergrad maths and
>> statistics)?
>>
>
> My idea of proportionality ("proportional") and majoritarian satisfaction
> ("preferred") being two separate dimensions hasn't been formally
> investigated, but it makes sense.
>
Could you please give a simple example of the calculations of the normalized
Bayesian regret and majoritarian satisfaction.


>  If we consider those dimensions separate but constraining each other, then
> the question becomes how to measure utility (for majoritarian satisfaction)
> and degree of proportionality (for proportional representation). The
> question of how to measure and sum up utility goes right to the question of
> commensurability, and there are many different ways of measuring
> proportionality as well.

If you're interested, http://www.mcdougall.org.uk/VM/ISSUE20/I20P4.PDF lists
> some of them.

Thanks, that proved to be good reading.
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