The Possible Incomensurability of Utilities and the Learning of Goals - Bruce Edmonds

2. Arguments Against the Possibility

One might seek to claim that in any particular situation for any particular agent there must be a mapping onto a single utility function, but it is entirely unclear why this should be necessarily true. This may be readily believable in some situations, but that is very far from the assumption that this must be possible in all situations.

It may also be argued that agents do choose actions in such situations. This argument can be put in two forms.

Firstly, that this means that agents must reduce these to a single utility in order to have been able to make the decision. That this is not a strong argument can be shown by merely considering an alternative mechanism (e.g. as described in [7]).
Secondly, that these choices define the mapping to a single utility function in this particular context. This however begs the question. The purpose of the utility function is to explain and predict the choice of action. So if the utility function is explained in terms of the actual choice made, we are left with a circular explanation. Thus this is useless unless the explanation in one context can be used to predict the motivation or action in another context and although this may be true for certain restricted domains there is no evidence that this holds in general*1.

This leaves the possibility that the direction of explanation was intended to be in the reverse direction, i.e. that the observed actions were being used to explain the motivations of the agent. In this case, one is left with the question: "Why assume that the motivation can be reduced to one utility function?". There are several possible answers.

Firstly, simply because it is the simpler theory (a la Occam). This is an acceptable answer if the alternatives are equally plausible but I will argue otherwise below - namely that the existence of practically incommensurable utilities does explain some observed characteristics of action where a single utility theory would not.
Secondly, for meta-theoretical reasons, for example the fact that in many situations the assumption that the action of agents can be characterised by the optimization of a single utility (or a set of utilities that can be practically reduced to a single utility) enables one to prove desirable outcomes such as single equilibria. In this case the strength of the assumption lies in the extent to which these outcomes are actually observed (otherwise one is merely studying an obscure branch of mathematics and not anything which could be called a natural science) and the evidence for many of these in many situations is, to say the least, weak.
Thirdly, because many different goods and many kinds of wealth are routinely mapped into the single measure represented by money. However, this does not mean that the motivation for the decisions that agents make are reducible to a single utility function, just that for some kinds of transactions it is the only medium of exchange practically available. For example, it occurs that firms agree to exchange research intelligence rather than buy or licence it from each other. Now while one can legitimately delimit the subject of economics to transactions to do with money, this does not mean that these transactions can be adequately explained or predicted in terms of a single utility in monetary terms. For example marriage can have great monetary consequences but this does not mean a decision to marry can be adequately determined by a process of two individuals each seeking to maximise effectively single utilities*2.

In order to make this possibility of incommensurability more real, let us consider an example. Imagine two people playing chess. Each player's goal is to win and not lose. In the early stages of the game the players have to make decisions as to choices of action without there being any possibility of being able to work out all the consequences of their actions. However, this does not mean that they make arbitrary moves - typically they will judge the possible chess positions using a number of ad hoc indicators (number of pieces, how far up the board their pawns have progressed, how many central squares they control, time they have left on the clock etc.). Since the goal of winning is too abstract to motivate any planning at this stage of the game, maximising these indicators take on the role of effective goals (ones that plans and actions can be meaningfully traced back to).

Now, is there any meaningful sense in which these indicators can be said to be commensurable? Could the actions of these players (at this stage of the game) be characterised in terms of a model of optimising a single utility function? I think the answer to both questions is "no". While it is true that a certain player in a certain position may judge there to be a certain trade-off between these various indicators, this trade-off may vary substantially for different positions, and against different players. It might even vary between different matches even if the game has reached the same position against the same player! This strongly suggests that the particular trade-off is result of the decision making process rather than representing its motivation in any meaningful way. Likewise a model of decision making in terms of a process of maximising a single utility that is so context-dependent is unlikely to have any explanatory or predictive value.

The Possible Incomensurability of Utilities and the Learning of Goals - Bruce Edmonds - 05 SEP 97

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