[Election-Methods] Determining representativeness of multiwinner methods

[Howard]

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.

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

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.

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.

Kristofer Munsterhjelm wrote:
>> How do see the role of parties here? Do you use e.g. a binary
>> decision between left wing and right wing? Or maybe support or no
>> support to party P? Or maybe you don't measure party support at all
>> but just separate binary questions.
> 
> Parties aren't explicitly included. Implicitly and ideally, a party would 
> be a vector quantization center in issue-space, which is to say, a 
> provider of a popular combined platform. In reality, parties aren't 
> perfect and face distortions both because of their own nature and 
> because of the dynamics of the environment in which they exist.
> 
> The latter should be well known to list readers - one dynamics 
> example is that of Duverger's law. Another would be the median voter
> theorem for what election method is being used. I think Warren Smith
> argued that any preferential election method would produce a 2:3:2 
> ratio on a one-dimensional political spectrum - one major party and two
> lesser ones - but I can't verify that.
> 
> But to get back to the question: The binary issues are issues. Parties 
> present issue-bundles and therefore don't relate to the model. As such, 
> the model is more simple than reality, but not enough to invalidate it.
> 
> In an approval-type scenario, some of the binary issues could be 
> support/no support (as you say) above pure issue-agreement, but since 
> Hamming distance measures all differences equally, that means party 
> loyalty is the same for all parties with regard to all other parties. It's 
> better, I think, to just leave the parties as issue-bundles.
> 
>> Any opinions on how to treat different levels of importance of 
>> different criteria to the voter (and to the candidates)?
> 
> There are two questions here. I'm not sure which you mean, so I'll 
> answer them both.
> 
> The first is how much inter-issue differences matter in contrast to 
> intra-issue differences. To take an individual example, consider a 
> picky people that isn't bothered if the assembly is slightly disproportionate 
> on any issue, but finds the assembly unworthy if it errs very much 
> on a single issue. This is the matter which changes based on what
> error measure is used. I don't know which error measure is closest 
> to reality, so in keeping with the simple nature of the model, I used
> RMSE. One could argue in favor of, and use, absolute error, the 
> Sainte-Lague index, Gini, or many others.
> 
> The second is of how to handle the case where some issues are
> unimportant to a voter. A simple extension to the binary issue profiles 
> would be a ternary profile: 1 for agree, -1 for disagree, and 0 for no 
> opinion. Then one could count the discrepancy of assembly and 
> people on each issue, taking only into account those who have an 
> opinion (in either assembly or among the people), kind of like the 
> "no opinion" score in Range. But what does it mean for an assembly 
> to have no opinion on a single issue? Directly speaking, it means that 
> they don't consider the issue, it takes no part in the deliberation. But 
> how does one compare the "error" of the assembly with regards to 
> the people in that case? I don't have an answer to that, so I didn't 
> implement it. (Perhaps it'd count maximally, since both those in 
> favor and against would be unhappy? Perhaps it'd count as if it was 
> 50%, assuming the assembly members would make decisions that
> impact this issue randomly, half the time in support by coincidence,
> and half the time against it by coincidence...) 
> 
>> How about traditional party list based multi-winner methods? I find
>> methods that allow candidates to form a tree like structure (instead
>> of the typical flat party structure) where different branches reflect
>> different opinions on different key questions interesting from this
>> proportionality point of view.
> 
> Party list needs parties, and there's also the question of open versus 
> closed list. Both open and closed list have to have a list in the first 
> place, and the nature of that list is complex, often shaped by the 
> interplay of power within the party.
> 
> But perhaps parties could be added by having a "preround" where
> one runs k-means clustering (vector quantization codebook 
> generation) to find the best party platforms, and then create lists 
> based on distance from that platform, where voters vote on the 
> list according to the platform's distance from their own views. 
> That would be complex, but yes, interesting. Such a party model 
> would also support simulations of "voting above the line" and MMP,
> but again I'm not sure whether the results would be close enough
> to reality to be any good.
> 
> What do you mean by "methods that allow candidates to form a 
> tree like structure"? Something like delegable proxy, or just 
> preference ballots with parties instead of candidates? Or 
> nontraditional nested democracy (groups elect members to an 
> assembly - groups of assemblies elect members to a second-
> level assembly, onwards up to global issues)?
> 
>> One more observation. Nowadays many methods actually try to meet two
>> kind of proportionality requirements, political/ideological
>> proportionality (typically based on the party structure) and regional
>> proportionality (typically implemented by mandating all to vote at
>> their own home district for the local candidates there). These
>> scenarios may be out of the scope of the proposed metric because of
>> the mandated nature of the regional representation, but regional
>> proportionality is one interesting and maybe also measurable
>> criterion for proportionality.
> 
> That sounds like MMP (vote for party, and vote for local candidates). 
> It's out of scope of the metric itself, as I envisioned it being used to 
> find out which party-neutral election method would be the best. 
> 
> If we assume that the mixed-member proportional method uses local 
> lists for the party-list aspect of the method, then the regional 
> disproportionality is independent of the constituency outcome, since 
> whatever the constituency outcome, the seats of a constituency are 
> only contested by candidates within the region in question. Thus the 
> strict regional proportionality would be decided by the party-list aspect, 
> such as by rounding error interactions between region size and 
> nationwide party support.
> 
> Still, one could imagine a less "artificial" geographical representation 
> metric. Make a density map of the candidates, and then one of the 
> electorate. Normalize both, and the more similar the maps are to each 
> other, the better. Or, for each voter, add the distance between him and 
> the closest elected candidate, and the lower the sum, the better. For 
> the metric to have anything to measure, the voter would either have to 
> directly prefer local candidates (by how much?) or the election method 
> knows where the various voters and candidates live.
> 
> In general, it seems like MMP-type systems are methods where 
> voters don't just vote on candidates, but also on properties. These can
> be party (in traditional MMP), or location (in the odd hypothetical 
> "knows where the voters live" method of the previous paragraph).
> 
> But this reply is getting long and I'm offtopic, so I'll end here. I tend 
> to answer speculation with speculation :-)
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