[EM] Spatial models -- Polytopes vs Sampling

[Daniel Carrera]

On Fri, Feb 4, 2022 at 5:05 AM Colin Champion
<colin.champion at routemaster.app> wrote:

> I haven't followed this discussion - sorry if I'm missing something. I
> quite like Jameson Quinn's model of an infinite number of dimensions of
> progressively diminishing importance. On the other hand, if 'n
> dimensions' is understood as meaning n dimensions of equal importance,
> then it seems to me intuitively unattractive. As a first approximation I
> might describe politics on a left/right axis; as a second I might
> distinguish between economic and social liberalism but expect them to be
> correlated (leading to a cigar-shaped 2D Gaussian) etc. (This doesn't
> help Daniel who wants an upper limit.)
>


That's my intuition as well --- dimensions of decreasing importance. If you
wanted to make a cigar-shaped Gaussian, do you have any idea of how
elongated it should be? Like... should each dimension have half the
variance of the one before? Something else?

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.



> Quinn's model is on his vse page:
> http://electionscience.github.io/vse-sim/VSE/
>

I've read this page before and I dismissed it because I couldn't figure out
what the model actually was. Maybe it's obvious and I just don't see it,
but what is the actual formula for the VSE?

But in any case, the current conversation is about dimensionality, so you
are thinking of the “Hierarchical clusters” model, right?

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