[EM] Spatial models -- Polytopes vs Sampling

[Daniel Carrera]

On Fri, Feb 4, 2022 at 3:38 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> I found a (very rough draft of a) paper that argues that political
> positions are hierarchical down to infinity, i.e. that if you ask very
> specific questions, different voters will have different opinions about
> these, but that they can be grouped into larger categories that do make
> sense in lower dimensional space.
>
>
> https://garymarks.web.unc.edu/wp-content/uploads/sites/13018/2016/09/rovny-and-marks.-issues-and-dimensions.pdf
>
> If that's true, then there should be some kind of effective limit to the
> number of dimensions given by the degree that voters care to coordinate
> and know the issues, and how strong a low-pass filter (so to speak) the
> political mechanism provides. PR would allow for more distinctions than
> FPTP.
>

Thanks for the link! I'll read it over the weekend.




> I don't know what this natural level would be, though, for something
> like Condorcet. I guess it would depend on to what degree dimensions
> follow geographical distinctions: if six districts have voters who care
> exclusively about economic issues, and four districts care exclusively
> about unitary state vs devolution issues, then that's going to give a
> different composition of issue space than if the unitary/devolved voters
> are represented by 40% in every district and the economic voters by 60%
> also in every district.
>

Yeah. The eternal problem of single-member districts. One feature that I
like about STV compared to other PR methods (and I realize STV is not 100%
PR) is that in principle STV is sensitive to dimensions that might not be
represented by political parties. If an electorate wants more women in
power, STV can produce that without there necessarily being a "women's
party".


> Let me also respond to Kristofer's comment about not taking the current
> > bungling of issues as a given. One could argue that the pragmatic
> > approach is to ask how a change in the electoral system would affect the
> > fortunes of minor parties that already exist, or how it might encourage
> > a new party to form. In the former case, you only need to model the
> > sub-space spanned by parties that already exist, and in the latter you
> > only need 1 more dimension than that.
>
> Yes. But if we're not careful, that's the kind of reasoning that leads
> to IRV-type reform. Suppose that a method is stable for k parties and
> then something bad happens at k+1. Once we're stuck at k parties, we may
> ask for a reform that brings the well-behaved regime up to k+1. But then
> we'll have the same problem at k+1.
>

Oh... Right... Yeah... I didn't think of that. Yeah, we need to make sure
election methods have room to grow.



> The concept of VSE is simply this:
>
> Suppose every voter assigns an absolute utility to each candidate. Then
> each candidate provides the electorate as a whole with some amount of
> total utility, were he elected.
>
> Now suppose there's a magic method that reads the voters' minds and
> always elects the best candidate.


How do we decide who the best candidate is? Is it the one that maximizes
total utility? I'm not sure I buy into the utilitarian argument. If making
one person really miserable will make 10 people really happy, I would not
necessarily consider that a good outcome. I'm also skeptical of the idea
that one person's vote matters more if they feel more strongly about it.
And that's not even taking into account the possible damage that a small
extremist wing can have just by virtue of being extremist.

To put it differently, if moral philosophers cannot agree that
utilitarianism is the way to go, why do I think that I can write an
algorithm that solves the utilitarian problem?

Concorcet and PR methods are nice in that they strike a balance between
taking into account as much of the voter's preferences as possible without
getting into the whole mess of computing utilities.

Btw, thanks for the links. I'll go read those too.

Cheers,
-- 
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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