[EM] Proportionality vs utility: Droop quota and feasible points

[Kristofer Munsterhjelm]

On 2024-09-14 23:47, Toby Pereira wrote:
> The problem is that we can't objectively determine utilities from the 
> scores. We can only make models that make assumptions. I don't think 
> using total score in the trade-off is necessarily bad a thing because 
> it's something we can easily objectively measure; I just don't think 
> it's correct to call it "utility".

Every model relies on *some* assumptions. Even the ordinary sort of VSE 
that puts Range on top assumes that the quality of the winner can be 
based on the sum of the voters' utilities (as opposed to, say, Rawlsian 
leximin), and that temporal effects don't matter.

That said, I'm not terribly wedded to the term. My first thought was 
"majoritarian satisfaction", but it's not really majoritarian.

This "utility" has the property that, assuming the validity of its 
single-winner version, a method that has more of it with the same 
proportionality is better, and a method that has more proportionality 
with the same "utility" is also better. It thus necessarily reduces to 
ordinary VSE in the single-winner case. Whatever term we come up with 
for it should capture this, and ideally be relatively short too.

The reason I first chose this as one of the axes is that it's obviously 
in tension with proportionality, and that the two axes reflect the 
spread of possible solutions between "have a lot of individually good 
winners who everybody likes" and "specialize by having some winners who 
appeal to some people, others appealing to others" that comes with PR.

Somewhere on this tradeoff curve there's an optimum, but I suspect that 
the location of that optimum depends on a bunch of parameters we don't 
know. It's possible to argue reasonably for single-winner districts 
filled with something like Condorcet (or Range if you're a cardinal 
guy); and it's possible to argue reasonably for proportional 
representation and the specialization that comes with it. See e.g. 
https://betterchoices.vote/ for the former and 
https://protectdemocracy.org/work/can-proportional-representation-create-better-governance/ 
for the latter.[1]

If we don't know the optimum, the best we can do is provide a 
high-quality method with a tunable parameter that decides the "utility" 
vs proportionality tradeoff. Choose-one party list PR isn't it: due to 
Plurality's vote-splitting problems, going from Sainte-Laguë to D'Hondt 
doesn't give more power to centrists who could break problematic 
kingmaker scenarios, it just gives more power to the large-bloc parties.

-km

[1]  Furthermore, I suspect that even if we could gather all the data 
for the parameters to determine the optimum, the resulting process would 
be very opaque, which is a problem in itself.