In dealing with your example, I didn’t “change the space of states or choices”. All I did was specify a utility function. The input states and output states were exactly as you specified them to be. The agent could see what choices were available, and then it picked one of them—according to the maximum value of the utility function I specified.
The corresponding real world example is an agent that prefers Boston to Atlanta, Chicago to Boston, and Atlanta to Chicago. I simply showed how a utility maximiser could represent such preferences. Such an agent would drive in circles—but that is not necessarily irrational behaviour.
Of course much of the value of expected utility theory arises when you use short and simple utility functions—however, if you are prepared to use more complex utility functions, there really are very few limits on what behaviours can be represented.
The possibility of using complex utility functions does not in any way negate the value of the theory for providing a model of rational economic behaviour. In economics, the utility function is pretty fixed: maximise profit, with specified risk aversion and future discounting. That specifies an ideal which real economic agents approximate. Plugging in an arbitrary utility function is simply an illegal operation in that context.
In dealing with your example, I didn’t “change the space of states or choices”. All I did was specify a utility function. The input states and output states were exactly as you specified them to be. The agent could see what choices were available, and then it picked one of them—according to the maximum value of the utility function I specified.
The corresponding real world example is an agent that prefers Boston to Atlanta, Chicago to Boston, and Atlanta to Chicago. I simply showed how a utility maximiser could represent such preferences. Such an agent would drive in circles—but that is not necessarily irrational behaviour.
Of course much of the value of expected utility theory arises when you use short and simple utility functions—however, if you are prepared to use more complex utility functions, there really are very few limits on what behaviours can be represented.
The possibility of using complex utility functions does not in any way negate the value of the theory for providing a model of rational economic behaviour. In economics, the utility function is pretty fixed: maximise profit, with specified risk aversion and future discounting. That specifies an ideal which real economic agents approximate. Plugging in an arbitrary utility function is simply an illegal operation in that context.