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

[Kristofer Munsterhjelm]

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.

> 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.

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.

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.