The OP claims that the policy “if I previously turned down some option X, I will not choose any option that I strictly disprefer to X” escapes the money pump but “never requires them to change or act against their preferences”.
But it’s not clear to me what conceptual difference there is supposed to be between “I will modify my action policy to hereafter always choose B over A-” and “I will modify my preferences to strictly prefer B over A-, removing the preference gap and bringing my preferences closer to completeness”.
Ah yep, apologies, I meant to say “never requires them to change or act against their strict preferences.”
Whether there’s a conceptual difference will depend on our definition of ‘preference.’ We could define ‘preference’ as follows: an agent prefers X to Y iff the agent reliably chooses X over Y.′ In that case, modifying the policy is equivalent to forming a preference.
But we could also define ‘preference’ so that it requires more than just reliable choosing. For example, we might also require that (when choosing between lotteries) the agent always take opportunities to shift probability mass away from Y and towards X.
On the latter definition, modifying the policy need not be equivalent to forming a preference, because it only involves the reliably choosing and not the shifting of probability mass.
And the latter definition might be more pertinent in this context, where our interest is in whether agents will be expected utility maximizers.
But also, even if we go with the former definition, I think it matters a lot whether money-pumps compel rational agents to complete all their preferences up front, or whether money-pumps just compel agents to resolve preferential gaps over time, conditional on them coming to face choices that are arranged like a money-pump (and only completing their preferences if and once they’ve faced a sufficiently diverse range of choices). In particular, I think it matters in the context of the shutdown problem. I talk a bit more about this here.
If it doesn’t move probability mass, won’t it still be vulnerable to probabilistic money pumps? e.g. in the single-souring pump, you could just replace the choice between A- and B with a choice between two lotteries that have different mixtures of A- and B.
I have also left a reply to the comment you linked.
Making a similar point from a different angle:
The OP claims that the policy “if I previously turned down some option X, I will not choose any option that I strictly disprefer to X” escapes the money pump but “never requires them to change or act against their preferences”.
But it’s not clear to me what conceptual difference there is supposed to be between “I will modify my action policy to hereafter always choose B over A-” and “I will modify my preferences to strictly prefer B over A-, removing the preference gap and bringing my preferences closer to completeness”.
Ah yep, apologies, I meant to say “never requires them to change or act against their strict preferences.”
Whether there’s a conceptual difference will depend on our definition of ‘preference.’ We could define ‘preference’ as follows: an agent prefers X to Y iff the agent reliably chooses X over Y.′ In that case, modifying the policy is equivalent to forming a preference.
But we could also define ‘preference’ so that it requires more than just reliable choosing. For example, we might also require that (when choosing between lotteries) the agent always take opportunities to shift probability mass away from Y and towards X.
On the latter definition, modifying the policy need not be equivalent to forming a preference, because it only involves the reliably choosing and not the shifting of probability mass.
And the latter definition might be more pertinent in this context, where our interest is in whether agents will be expected utility maximizers.
But also, even if we go with the former definition, I think it matters a lot whether money-pumps compel rational agents to complete all their preferences up front, or whether money-pumps just compel agents to resolve preferential gaps over time, conditional on them coming to face choices that are arranged like a money-pump (and only completing their preferences if and once they’ve faced a sufficiently diverse range of choices). In particular, I think it matters in the context of the shutdown problem. I talk a bit more about this here.
If it doesn’t move probability mass, won’t it still be vulnerable to probabilistic money pumps? e.g. in the single-souring pump, you could just replace the choice between A- and B with a choice between two lotteries that have different mixtures of A- and B.
I have also left a reply to the comment you linked.