[EM] Spatial models -- Polytopes vs Sampling

[Kristofer Munsterhjelm]

On 04.02.2022 03:43, Forest Simmons wrote:

>>    It's good to have a maximum. I hope we can get away with fewer than
>>    8 dimensions. Regardless of the true political dimensions of the
>>    electorate, if you only have N<8 parties, those parties will lie in
>>    an (N-1)-dimensional subspace. That's why I suspect that we can get
>>    away with modelling a lot less than 8D and just be aware that I'm
>>    only modelling the subspace of political positions that is actually
>>    spanned by the candidates. The US is a specially pathological
>>    example, where apparently your views on LGBT rights somehow dictate
>>    your views on sex education, AR-15s, tax law, climate change,
>>    vaccines, and the Israel-Palestine conflict.
> 
> 
> PR is supposed to help fix this, but ingrained traditions are hard to
> buck ... and (obviously) PR has no chance at all of helping if we never
> adopt it.

Yeah, my reluctance to base dimensions around the number of currently
existing parties in part stems from this. If we're supposed to improve
the state of politics, then we shouldn't take the current bundling of
issues as a given. To the degree it's possible, the method should get
out of the voters' way and let the natural number of dimensions reveal
itself through their actions.

FPTP doesn't do this.

Poll data would presumably be less contaminated by the
squashing-together effect of two party rule than actual election results
would be; and the results from New York's STV era also suggest that
there's room for multiple parties if the method just allows them to exist.

On another side note, I examined JGA's strategy paper a bit more closely
and I see that he has another synthetic model (IAC) which matches the
poll data well, at least for strategic resistance. I could check whether
it's as easy to construct exact probabilities for IAC as it is for IC; I
would expect so, since it's statistically very simple. However, I
couldn't easily construct exact probabilities for the utilities since
draws from a normal distribution need not be rational.

Perhaps if we make a method whose minimum VSE over a linear combination
of high dimensional spatial and IAC is maximized, we would have a
generally good method without overfitting *too* much. Same with
maximizing minimum relative strategy resistance, or some combination of
the two.

I say "make", but it's not that easy. The strategy generator could
possibly be fitted to do this, but inferring structure out of its lookup
table is still very hard, as I've said.

-km