Side question: the “risky” axioms seem quite similar to the Archimedean axiom in some variants of the VNM utility theorem. I think you also assume completeness and transitivity – are they enough to recover the entire VNM theorem? (I.e. do your axioms imply that there is a real-valued utility function whose expectation we must be trying to maximize?)
This is interesting. It looks like the risky versions would follow from the Archidemean axiom + their non-risky vesions.
I don’t think you could get the independence axiom from the other axioms, though. Well, technically anything satisfying all of the axioms would satisfy independence, since nothing satisfies all of the axioms, since it’s an impossibility theorem, but if you consider only the risky axioms (or the Archimedean axiom), completeness and transitivity, I don’t see how you could get the independence axiom. Maybe maximizing the median value of some standard population axiology like total utilitarianism is a counterexample?
This is interesting. It looks like the risky versions would follow from the Archidemean axiom + their non-risky vesions.
I don’t think you could get the independence axiom from the other axioms, though. Well, technically anything satisfying all of the axioms would satisfy independence, since nothing satisfies all of the axioms, since it’s an impossibility theorem, but if you consider only the risky axioms (or the Archimedean axiom), completeness and transitivity, I don’t see how you could get the independence axiom. Maybe maximizing the median value of some standard population axiology like total utilitarianism is a counterexample?
Thanks! Your points about independence sound right to me.