The Possible Incomensurability of Utilities and the Learning of Goals - Bruce Edmonds
that a single agent might simultaneously have different utilities that are incommensurable.That is, not just that the different utilities the agent is seeking are independent or even conflicting but that there is no meaningful mapping from these different utilities to a single utility function, even a single ordinal utility ranking. In other words that the utilities may be of fundamentally different kinds so that any mapping to a single measure could only be made by losing the essential nature of one of them. This is in direct contradiction with the assumptions of many economic models e.g. [6] and goes beyond attempts to merely explain or fix intransitivity of choices (as in [1]).
For example, one can imagine an agent which wished to maximise both income and love. Now one can imagine that these two utilities could be incommensurable - that is that there might be no mapping between the two so that the agent could meaningfully translate amounts of love into income or vice versa. Now further suppose that in a certain situation there was no action that simultaneously maximised both indicators, but that there were actions that maximised one or the other - this is often the case. In such a situation there would be no single action that would represent an optimum. The agent might have to choose between a range of actions, some of which resulted in it gaining income and some which resulted in it gaining love. In other words there might be no single numerically valued utility function which the agent could be said to be attempting to optimise, i.e. it would not even be the case that the agent was acting as if it were seeking to optimise a single utility function.
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