That only demonstrates that the deontologist can make less money than they would without their rules. That is not money pumping. It is not even a failure to maximise utility. It just means that someone with a different utility function, or a different range of available actions, might make more money than the deontologist. The first corresponds to giving the deontologist a lexically ordered preference relation.[1] The second models the deontologist as excluding rule-breaking from their available actions. A compromising deontologist could be modelled as assigning finite utility to keeping to their rules.
This is not consistent with the continuity axiom of the VNM theorem, but some people don’t like that axiom anyway. I don’t recall how much of the theorem is left when you drop continuity.
That only demonstrates that the deontologist can make less money than they would without their rules. That is not money pumping. It is not even a failure to maximise utility. It just means that someone with a different utility function, or a different range of available actions, might make more money than the deontologist. The first corresponds to giving the deontologist a lexically ordered preference relation.[1] The second models the deontologist as excluding rule-breaking from their available actions. A compromising deontologist could be modelled as assigning finite utility to keeping to their rules.
This is not consistent with the continuity axiom of the VNM theorem, but some people don’t like that axiom anyway. I don’t recall how much of the theorem is left when you drop continuity.