[EM] An impractical suggestion for redistricting

[Kristofer Munsterhjelm]

On 6/10/22 12:52 PM, Colin Champion wrote:
> On 08/06/2022 14:09, Kristofer Munsterhjelm wrote:
> I was reading https://arxiv.org/pdf/1901.04628.pdf, which gives an 
> approximation to hard capacitated k-means clustering (basically, 
> districting with the constraint that each district population should be 
> the same)...
> 
> In the UK, constituencies are adjusted by a commission. I don't suppose 
> it's perfectly fair but in practice the errors it gives rise to are 
> tolerably small. There's a bigger problem: constituencies are either 
> rural or urban. If rural constituencies favour party A by a small 
> majority and urban constituencies favour B by a large majority, then A 
> has an in-built advantage. I'm not aware of anything in k-means 
> clustering which guards against this.

It doesn't, no. It replaces engineered biases with natural ones (which 
seem to be less severe, e.g. https://arxiv.org/abs/1410.8796).

Any constituency-based majoritarian system has a fundamental limitation 
in that it doesn't give parties who have a little representation 
everywhere its share of the seats. Presumably better single-winner 
voting methods like Condorcet would allow these minor factions to drag 
the center in their direction, but it wouldn't give them direct 
representation.

You could add a districting step to a Monroe-type multiwinner election 
so that it draws "districts" of voters each candidate is accountable to, 
after the fact, but I don't really see what the point would be :-) 
Imposing the required geographic contiguity constraints would lower the 
proportionality of the result, as well.

-km