(And by "any reason" I guess I mean "any reason besides lack of comfort with non-whole numbers").
From here it seems like the general principle of social cost still applies / doesn't have anything to do with the step-function nature of things.
In Weyl and Posner's book "Radical Markets" they motivate quadratic voting as outlined as a way of preference voting where a voter's desire intensity is represented in the vote.
Their argument is practically outlined in the pollution + city example I make in the original blog post and where, with the sloppy figure I have attached [1], they reason geometrically that "Nils" should "pay" for reducing the electricity plant's pollution. If you look closely at that figure (which is nicer in the book), you can see that the plane where the cost functions intersect is a triangle.
I can't fully reproduce the mathematical reasoning here, but how I understood it is that dependent on Nils's choice, the externality he imposes has quadratic cost given that the triangle's change is affected quadratically. In an isosceles triangle, where volume V is defined dependent on two same length sides, I can see that work out. But I've never worked through that.
More intuitively, an example, I'm just making up is if you're annoyingly snorting during a visit to the cinema.
If you're the only person snorting and you think that's OK, but nobody else can understand the dialogue - you're not only wasting your money but everybody else's. It's quadratic because of the opportunity cost of everybody wasting 2 hours but having all paid for the film. So both the cost of the cinema running the movie for two hours and everybody paying but not understanding makes your snorting square the cost. Does that make sense? Please correct me if I'm wrong.
So essentially, if Nils is picky with anti-pollution, his pickiness costs the town's society quadratically - which is why he should pay the quadratic cost of his pickiness during governance.
references:
- 1: https://timdaub.github.io/assets/images/cost-of-externality....