Ah yes, nice point. The policy should really be something like ‘if I previously turned down some option X, then given that no uncertainty has been resolved in the meantime, I will not choose any option that I strictly disprefer to X.’ An agent acting in accordance with that policy can trade y for X−.
And I think that even agents acting in accordance with this restricted policy can avoid pursuing dominated strategies. As your case makes clear, these agents might end up with X− when they could have had X (because they got unlucky with Y yielding y). But although that’s unfortunate for the agent, it doesn’t put any pressure on the agent to revise its preferences.
I think a multi-step decision procedure would be better. Do what your preferences themselves tell you to do and rule out any options you can with them. If there are multiple remaining incomparable options, then apply your original policy to avoid money pumps.
Ah yes, nice point. The policy should really be something like ‘if I previously turned down some option X, then given that no uncertainty has been resolved in the meantime, I will not choose any option that I strictly disprefer to X.’ An agent acting in accordance with that policy can trade y for X−.
And I think that even agents acting in accordance with this restricted policy can avoid pursuing dominated strategies. As your case makes clear, these agents might end up with X− when they could have had X (because they got unlucky with Y yielding y). But although that’s unfortunate for the agent, it doesn’t put any pressure on the agent to revise its preferences.
I think a multi-step decision procedure would be better. Do what your preferences themselves tell you to do and rule out any options you can with them. If there are multiple remaining incomparable options, then apply your original policy to avoid money pumps.