[EM] Proportionality vs utility: redoing 2008 with better units

[Kristofer Munsterhjelm]

Posting again because EM was having trouble yesterday:

On 2024-09-16 19:08, Toby Pereira wrote:
> I was just thinking that if I was doing a total score (what we're 
> calling utility here) versus proportionality graph, for proportionality 
> I might just use the var-Phragmen measure + KPT off the voter's utility 
> scores, rather than taking the further step of looking at what the 
> elected candidates would do once elected. I generally think that 
> var-Phragmen gives the best measure of proportionality (and it reduces 
> to Sainte-Laguë).

I am a bit wary of doing so because I prefer using hidden information to 
determine the methods' quality. Similar to how Borda's high VSE isn't 
obvious (particularly given its center bias), it may not be obvious what 
method is best at being proportional in issue space.

Linking the optimum to a particular method carries the risk of blinding 
us to whether some other method is better at it. We wouldn't want to, 
for instance, define methods' utilitarian quality as their outcomes' 
Kendall tau distance from Borda.

If the strange apparent small-opinion bias persists with different 
models, I may have to reconsider. But I think I'll try other models 
before I link the optimum to a concrete method.

-km