More generally, suppose that the agent acts in accordance with the following policy in all decision-situations: ‘if I previously turned down some option X, I will not choose any option that I strictly disprefer to X.’ That policy makes the agent immune to all possible money-pumps for Completeness.
Am I missing something or does this agent satisfy Completeness anytime it faces a decision for the second time?
I don’t think so, Suppose the agent first chooses A when we offer it a choice between A and B. After that, the agent must act as if it prefers A to B-. But it can still lack a preference between A and B, and this lack of preference can still be insensitive to some sweetening or souring: the agent could also lack a preference between A and B+, or lack a preference between A+ and B, or lack a preference between B and A-.
What is true is that, given a sufficiently wide variety of past decisions, the agent must act as if its preferences are complete. But depending on the details, that might never happen or only happen after a very long time.
If you’re interested, these kinds of points got discussed in a bit more detail over in this comment thread.
Am I missing something or does this agent satisfy Completeness anytime it faces a decision for the second time?
I don’t think so, Suppose the agent first chooses A when we offer it a choice between A and B. After that, the agent must act as if it prefers A to B-. But it can still lack a preference between A and B, and this lack of preference can still be insensitive to some sweetening or souring: the agent could also lack a preference between A and B+, or lack a preference between A+ and B, or lack a preference between B and A-.
What is true is that, given a sufficiently wide variety of past decisions, the agent must act as if its preferences are complete. But depending on the details, that might never happen or only happen after a very long time.
If you’re interested, these kinds of points got discussed in a bit more detail over in this comment thread.