I think this model’s assumptions are not just counterintuitive (as other commenters have noted) but internally contradictory.
Three premises:
All VNM axioms except for Continuity.
For some small amount of intense suffering, there is always some sufficiently large amount of moderate suffering such that the intense suffering is preferable.
Small amounts of suffering can be offset by sufficiently large amounts of happiness.
Some people would reject #2 but if I understand correctly, your model takes all three of these premises as true.
Suppose world W has probability p of a large amount of moderate suffering, plus probability (1 - p) of an amount of happiness sufficient to offset it.
Let world W’ have probability (1 - p) of the same amount of happiness but probability p of a smaller amount of intense suffering, such that the intense suffering in W’ is preferable to the moderate suffering in W.
By the Independence axiom, W’ must be preferable to W, and therefore W’ is net positive, which means arbitrarily intense suffering can be offset by happiness.
For some small amount of intense suffering, there is always some sufficiently large amount of moderate suffering such that the intense suffering is preferable.
To be clear, I think this premise is one way of distilling and clarifying the (or ‘a’) crux of my argument and if I wind up convinced that the whole argument is wrong, it will probably be because I am convinced of premise 2 or something very similar
I see, I took the chart under “The compensation schedule’s structure” to imply that the Axiom of Continuity held for suffering, based on the fact that the X axis shows suffering measured on a cardinal scale.
If you reject Continuity for suffering then I don’t think your assumptions are self-contradictory.
I think this model’s assumptions are not just counterintuitive (as other commenters have noted) but internally contradictory.
Three premises:
All VNM axioms except for Continuity.
For some small amount of intense suffering, there is always some sufficiently large amount of moderate suffering such that the intense suffering is preferable.
Small amounts of suffering can be offset by sufficiently large amounts of happiness.
Some people would reject #2 but if I understand correctly, your model takes all three of these premises as true.
Suppose world W has probability p of a large amount of moderate suffering, plus probability (1 - p) of an amount of happiness sufficient to offset it.
Let world W’ have probability (1 - p) of the same amount of happiness but probability p of a smaller amount of intense suffering, such that the intense suffering in W’ is preferable to the moderate suffering in W.
By the Independence axiom, W’ must be preferable to W, and therefore W’ is net positive, which means arbitrarily intense suffering can be offset by happiness.
I do not accept premise 2:
To be clear, I think this premise is one way of distilling and clarifying the (or ‘a’) crux of my argument and if I wind up convinced that the whole argument is wrong, it will probably be because I am convinced of premise 2 or something very similar
I see, I took the chart under “The compensation schedule’s structure” to imply that the Axiom of Continuity held for suffering, based on the fact that the X axis shows suffering measured on a cardinal scale.
If you reject Continuity for suffering then I don’t think your assumptions are self-contradictory.