Can utility be subjective?

A subjective (personal) utility function has no predictive power because subjective preferences can change in an arbitrary way. This does not mean that they do. But if they do, there is nothing irrational about an arbitrary change of subjective (personal) utility.

To see the significance of the above remarks, we should consider two related but substantially (perhaps fundamentally) different ways in which people think about utility. First, some psychologists, economists and other scientists use utility to explain human behavior that would appear irrational or unexplained if we used monetary units or "natural" units (such as "friends"). The theory of subjective utility can explain quite well some observed phenomena. Psychologists can determine typical subjective opinions and other scientists can build these opinions into their models of decision making. Some of these models fit very well with real data. The fact that subjective utility is more or less stable for each individual is sufficient to make such scientific models reasonably realistic.

The second way in which subjective utility is used, at least in the subjective philosophy of probability, is to guide an individual decision maker. The fact that the utility function can be unstable destroys the basic decision making principles. Of course, an individual can make a probabilistic prediction of his or her future subjective utility but this seems to make the model too complicated to be practical. Also, unstable utility completely destroys the Dutch book argument in situations involving non-monetary rewards.

Measuring objective utility (it there is such a thing) seems to be hard or impossible. Measuring subjective utility does not seem to be any easier, mostly because people often evaluate rewards in a context.

The following remarks apply to objective and subjective utilities. If one has to make a large number of i.i.d. decisions with financial rewards then one should use the nominal value of money in decision making, not utility. The reason is that if two decisions have expectations b dollars and c dollars, respectively, then after n decisions the wealth of the decision maker will be n b + o(n) if he always makes the first decision, and n c + o(n) if he always makes the second decision. In this example, assuming that the utility function is increasing, the optimal decision is the one which maximizes the expectation of the dollar reward. Note that, in general, this is not the same decision which maximizes the expected utility. Therefore utility functions may be useful only in situations when there are no long runs of i.i.d. decision problems. Here are some examples of such situations. (i) The decision maker is concerned only with a single decision or a small number of decisions. (ii) There are many decisions to be made and some decisions have disproportionately large consequences relative to others. (iii) The utility of a large number of non-monetary rewards is a complicated function of the rewards (what is the utility of having one million friends?).