You describe an agent that dodges the money-pump by simply acting consistently with past choices. Internally this agent has an incomplete representation of preferences, plus a memory. But externally it looks like this agent is acting like it assigns equal value to whatever indifferent things it thought of choosing between first.
Not sure I follow this / agree. Seems to me that in the “Single-Souring Money Pump” case:
If the agent systematically goes down at node 1, all we learn is that the agent doesn’t strictly prefer [B or A-] to A.
If the agent systematically goes up at node 1 and down at node 2, all we learn is that the agent doesn’t strictly prefer [A or A-] to B.
So this doesn’t tell us what the agent would do if they were faced with just a choice between A and B, or A- and B. We can’t conclude “equal value” here.
Not sure I follow this / agree. Seems to me that in the “Single-Souring Money Pump” case:
If the agent systematically goes down at node 1, all we learn is that the agent doesn’t strictly prefer [B or A-] to A.
If the agent systematically goes up at node 1 and down at node 2, all we learn is that the agent doesn’t strictly prefer [A or A-] to B.
So this doesn’t tell us what the agent would do if they were faced with just a choice between A and B, or A- and B. We can’t conclude “equal value” here.