[Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

Howard wrote:
> Question to Kristofer
> 
> do you see the "issues" that you start off with as orthogonal?
> i.e. do you see this only working in a world where the issues polled are 
> independent.

The simulation I wrote assumes this, since it picks the proportion in 
favor on each issue independently. The simulation-idea itself could work 
with non-orthogonal issues, where one programs the individual issue 
profile generator to select true on an issue with a probability that's 
correlated (or reversely correlated) with the probability of selecting 
true on some other issue.

The concept works with non-orthogonal issues. The implementation doesn't.

> also, how it would be decided what issues are polled? even in a 
> simulation this is important.

I take a best-case approach here: every voter knows the issue profiles 
of every candidate. That's not how it would happen in reality, but it 
can only make the simulated scores better than in reality, not worse.

> Ultimately there are a large election there are wide variety of issues 
> and it is impossible for any one candidate or voter to be aware of all 
> of them much less have an opinion on them all.

Perhaps there could be a switch where, if turned on, the simulation only 
compares subsets of issue profiles. A noise parameter would determine 
how large a subset is compared. One would have to make assumptions as to 
the correlation of subsets, though - do voters compare on the same 
subsets (what's being advertised, for instance), or do they compare on 
different subsets (their special interests)? In hoping that the results 
can be generalized, picking random subsets may suffice.

> I think the generalization you propose below to a range of values is 
> probably worth while.
> it might then also be able to address not only proportionality on views 
> of the legislature, but also proportionality on the thrust of the 
> legislature.
> i.e. it is all well and good to say you are for some position but if the 
> legislature never proposes a new law or regulation around this position 
> it is of little use to the people.

How would you treat the case where the assembly doesn't care about a 
certain issue, but the voters do? Range-style "only count those with an 
opinion" would produce an undefined proportion in favor of the issue at 
that point (because of a division by zero). I'm not sure what the best 
approach would be in that case.