[yorwba]

It's interesting that it's possible to achieve proportional representation with respect to geographic distribution and party votes simultaneously. (Though, as the article notes, Iceland falls short of this ideal.)

This makes me wonder: why stop at two? Some places have explicit quotas for different ethnic or religious groups as a compromise to avoid civil war. Could they use a tripoportional system?

And why not add in even more demographic variables? Age, gender, income, level of education, ... I suppose at some point it stops being a secret election because the number of voters sharing all attributes becomes too small, or the parliament would get unwieldily large trying to represent every hyperspecific constituency.

[themadryaner]

It is possible! But with more than two dimensions, you have to allow deviations from perfect proportionality to guarantee a solution exists. The more dimensions, the worse it gets, until eventually proportionality breaks down entirely. [1] defines a method to do this and simulates the results on an election where district and party seats are distributed proportionally and divvied up by gender proportionally. The result is a better national proportionality at the expense of worse local proportionality.

[1]: https://www.pnas.org/doi/10.1073/pnas.2109305119

[wqaatwt]

> Some places have explicit quotas for different ethnic or religious groups as a compromise to avoid civil war

That leads to very dysfunctional outcomes due to obvious reasons. When you vote for the same party/candidate just because they belong to the same religion/ethnicity (and such seats are very easy to monopolize) they a freehand to due to whatever they want. So what if they are exceptionally corrupt or incompetent? It’s not like your are going to vote for other side..

[lambertsimnel]

That's a fascinating suggestion!

> I suppose at some point it stops being a secret election because the number of voters sharing all attributes becomes too small, or the parliament would get unwieldily large trying to represent every hyperspecific constituency.

I'm not sure about that. Maybe I'm being too optimistic, but I'd like to think such a procedure could be run with a legislature of any fixed size, at the cost of the proportionality being increasingly inexact for smaller demographics. Furthermore, I suspect the representatives from any demographic would be elected partly with votes from other demographics. Anyway, the number of voters would presumably be thousands of times the number of representatives - see https://en.wikipedia.org/wiki/Cube_root_law - so any voting demographic with dedicated representation would at least be thousands of voters.

[thaumasiotes]

> It's interesting that it's possible to achieve proportional representation with respect to geographic distribution and party votes simultaneously.

That would be interesting, but it's not even possible to achieve one of those things by itself.