Hmm, and the population X also comes after, rather than having the m,p,k possibly depend on X. It does look like your conditions are more “uniform” than my proposal might satisfy, i.e. you get existential quantifiers before universal quantifiers, rather than existential quantifiers all last (compare continuity vs uniform continuity, and convergence of a sequence of functions vs uniform convergence). The original GNEP and NE axioms have some uniformity, too.
I think informal explanations of the axioms often don’t get this uniformity across, but that suggests to me that the uniformity itself is not so intuitive and compelling at all in the first place, and it’s doing a lot of the work in these theorems. Especially when the conditions are uniform in the unaffected background population X, i.e. you require the existence of an object that works for all X, that seems to strongly favour separability/additivity/the independence of unconcerned agents, which of course favours totalism.
Uniformity also came up here, with respect to Minimal Tradeoffs.
Yes, that all sounds right to me. Thanks for the tip about uniformity and fanaticism! Uniformity also comes up here, in the distinction between the Quantity Condition and the Trade-Off Condition.
Hmm, and the population X also comes after, rather than having the m,p,k possibly depend on X. It does look like your conditions are more “uniform” than my proposal might satisfy, i.e. you get existential quantifiers before universal quantifiers, rather than existential quantifiers all last (compare continuity vs uniform continuity, and convergence of a sequence of functions vs uniform convergence). The original GNEP and NE axioms have some uniformity, too.
I think informal explanations of the axioms often don’t get this uniformity across, but that suggests to me that the uniformity itself is not so intuitive and compelling at all in the first place, and it’s doing a lot of the work in these theorems. Especially when the conditions are uniform in the unaffected background population X, i.e. you require the existence of an object that works for all X, that seems to strongly favour separability/additivity/the independence of unconcerned agents, which of course favours totalism.
Uniformity also came up here, with respect to Minimal Tradeoffs.
Yes, that all sounds right to me. Thanks for the tip about uniformity and fanaticism! Uniformity also comes up here, in the distinction between the Quantity Condition and the Trade-Off Condition.