This section doesn’t really discuss why it’s argued to be irrational in particular in the pieces you cite. I think the main objection on the basis of irrationality by Greaves, et al. (2022) would be violating Stochastic Dominance (wrt the value of outcomes, if agent-neutral). Stochastic Dominance is very plausible as a requirement of rationality.
One response to the violation of Stochastic Dominance, given that it’s equivalent to the conjunction of Stochastic Equivalence[1] and Statewise Dominance[2], is that:
Statewise dominance is satisfied by DMRA, so this isn’t a problem.
Stochastic equivalence rules out sensitivity to statewise differences (beyond what can be captured by ignoring statewise information), so its mere assertion against DMRA seems pretty question-begging.
Or, we could use a modified version of difference-making that does satisfy Stochastic Dominance. Rather than taking statewise differences between options as they are, we can take corresponding quantile differences, i.e. A’s qth quantile minus B’s qth quantile, for each q between 0 and 1.[3]
Other objections from the pieces are barriers to cooperation and violating a kind of universalizability axiom, although these seem to be more about ethics than rationality, except in cases involving acausal influence.
The preorder satisfies Stochastic Equivalence if for each pair of prospects A and B such thatP[A∈S]=P[B∈S] for each subset of events S, A and B are equivalent.
Not sure I follow this but doesn’t the very notion of stochastic dominance arise only when we have two distinct probability distributions? In this scenario the distribution of the outcomes is held fixed but the net expected utility is determined by weighing the outcomes based on other critera (such as risk aversion or aversion to no-difference).
Even if we’re difference-making risk averse, we still have and should still compare multiple distributions of outcomes to decide between options, so SD would be applicable.
This section doesn’t really discuss why it’s argued to be irrational in particular in the pieces you cite. I think the main objection on the basis of irrationality by Greaves, et al. (2022) would be violating Stochastic Dominance (wrt the value of outcomes, if agent-neutral). Stochastic Dominance is very plausible as a requirement of rationality.
One response to the violation of Stochastic Dominance, given that it’s equivalent to the conjunction of Stochastic Equivalence[1] and Statewise Dominance[2], is that:
Statewise dominance is satisfied by DMRA, so this isn’t a problem.
Stochastic equivalence rules out sensitivity to statewise differences (beyond what can be captured by ignoring statewise information), so its mere assertion against DMRA seems pretty question-begging.
Or, we could use a modified version of difference-making that does satisfy Stochastic Dominance. Rather than taking statewise differences between options as they are, we can take corresponding quantile differences, i.e. A’s qth quantile minus B’s qth quantile, for each q between 0 and 1.[3]
Other objections from the pieces are barriers to cooperation and violating a kind of universalizability axiom, although these seem to be more about ethics than rationality, except in cases involving acausal influence.
The preorder satisfies Stochastic Equivalence if for each pair of prospects A and B such thatP[A∈S]=P[B∈S] for each subset of events S, A and B are equivalent.
If A statewise dominates (is at least as good in ever state as) B, then A is at least as good as B.
In other words, we replace A and B with their quantile functions, applied to the same uniform random variable over the unit interval [0, 1]. See also Inverse transform sampling—Wikipedia.
Not sure I follow this but doesn’t the very notion of stochastic dominance arise only when we have two distinct probability distributions? In this scenario the distribution of the outcomes is held fixed but the net expected utility is determined by weighing the outcomes based on other critera (such as risk aversion or aversion to no-difference).
Even if we’re difference-making risk averse, we still have and should still compare multiple distributions of outcomes to decide between options, so SD would be applicable.