Classical decision theory is built around a central "representation theorem": so long as an agent’s preferences meet certain basic conditions of coherence, we can construct a function that represents the agent’s preferences — in the sense that the agent prefers one prospect X over a second prospect Y if and only if the value that this function assigns to X is greater than the value that the function assigns to Y; and moreover, this function has a fundamentally expectational structure, in the sense that the value that this function assigns to an uncertain prospect is the weighted sum of the values that the function assigns to all the possible outcomes of that prospect — where the value of each of these possible outcomes is weighted by the probability that that prospect will have that outcome.
So for classical decision theory, everything flows from these basic conditions on coherent preferences. In turn, these coherence conditions are typically defended by means of "Dutch book" arguments, which seek to show that someone whose preferences violate these conditions of coherence would be willing to take out a set of bets that would guarantee a certain loss, no matter what happened.
My problem is, I like the general idea that when we’re not certain what situation we’re in, we should be guided by probabilities. (As Joseph Butler, one of my philosophical heroes, put it, "To us, probability is the very guide of life.") And intuitively, the most rational way of being guided by probabilities in making our choices or decisions is by making choices that have maximal expected value (using probabilities to define the concept of the "expected" value of a function in the normal way). But for various reasons, I can’t accept the classical decision theorist’s explanation of why we should maximize expected value.
Don’t get me wrong — it’s not that I think that being willing to accept a Dutch book is a rational thing to do! My problem is that on all the ways that seem remotely promising of understanding the relevant notion of "preferences", these fundamental conditions of coherence seem either wrong or at least unmotivated.
- Suppose that preferences are thought of as a kind of desires. Then it doesn’t seem to me to be incoherent or irrational in any way to have preferences that are intransitive or symmetric. Such conflicting desires are simply the normal condition of human life. (If your life does not contain such conflicting desires, I would have to doubt whether you belong to the same species as I do — if indeed you belong to a species at all!) Such conflicting desires, it seems to me, are no more irrational than it is irrational to have illusory sensory experiences that conflict with one’s considered beliefs.
- Suppose that preferences are thought of as a kind of disposition to choose. Then someone in a "Buridan’s Ass" situation might have a systematic disposition always to choose to go to the Left, even though really they are perfectly indifferent between Left and Right. So, even though they would always choose a course of action that involves a 100% chance of going Left over a course of action that involves a 100% chance of going Right, this is just an arbitrary way of making a choice in a Buridan’s Ass situation; and so they need not have any preference for a gamble that gives them a 50% chance of going Left over an otherwise exactly similar gamble that gives them a 50% chance of going Right.
- Suppose that preferences are thought of as a kind of evaluative judgment — i.e. as judgments about which prospects are all things considered better than others. The trouble here arises when we ask whether the relevant sort of judgment are judgments about which prospects are objectively better than others, or about which prospects are subjectively better. Either way, problems arise:
- Suppose that preferences are identified with judgments about which prospects are objectively better than others. But the objective goodness of a prospect surely does not depend on what it rational to expect its outcome to be, but on what its outcome actually is. So if one is rational, and one does not know for certain what the outcome of a prospect will be, one will not form any outright belief about how objectively good that prospect is; in particular, one will not form the outright belief that the objective goodness of that prospect is identical with its expected degree of objective goodness (indeed, there are many cases in which it is certain that the objective goodness of a prospect is not identical to its expected degree of objective goodness).
- Suppose that preferences are identified with judgments about which prospects are subjectively better than others. But then it seems to me more plausible to identify a prospect’s degree of subjective goodness, not with its expected degree of subjective goodness, but with its expected degree of objective goodness. But then we don’t seem to have any illuminating explanation of why subjective goodness should be defined in this way, rather than in any other way. If it is a prospect’s objective goodness that ultimately matters, then why does a prospect’s expected degree of goodness matter at all? We don’t seem to have made any progress with understanding the fundamental question.
Anyway, that’s the problem that I’ve realized that I need to worry about (I should thank Ned McClennen, who was my commentator at the recent Syracuse conference on Practical Reason for prodding me to think about it ….): I believe that rational choice should maximize the expectation of some sort of value, but I don’t seem to be able to avail myself of the classical decision theorist’s reason for believing this.
So what reason do I have to believe this? I’ll try to post something outlining my rough ideas about what this reason might be at some point in the near future.