And then we can make it worse still with infinitely many options :P
I+I+(1−1n)I=(3−1n)I, for n≥0
0.5(1−I)+I+0=0.5(1+I)
Here, each option in 1 is Pareto dominated and stochastically dominated by any option from 1 for larger n, and 2 is the only option which is not stochastically dominated. If you are not allowed to choose stochastically dominated options, then 2 is the only permissible option, despite being Pareto dominated by all the others. In general, though, I think you just want to go with something like “scalar utilitarianism” and allow yourself to choose stochastically dominated options when there are infinitely many of them, or else you may have no permissible options.
And then we can make it worse still with infinitely many options :P
I+I+(1−1n)I=(3−1n)I, for n≥0
0.5(1−I)+I+0=0.5(1+I)
Here, each option in 1 is Pareto dominated and stochastically dominated by any option from 1 for larger n, and 2 is the only option which is not stochastically dominated. If you are not allowed to choose stochastically dominated options, then 2 is the only permissible option, despite being Pareto dominated by all the others. In general, though, I think you just want to go with something like “scalar utilitarianism” and allow yourself to choose stochastically dominated options when there are infinitely many of them, or else you may have no permissible options.
Oh interesting, thanks for sharing. These are compelling counterexamples