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Causal models are a useful tool for reasoning about causal relations. Meek and Glymour 1994 suggested that they also provide new resources to formulate causal decision theory. The suggestion has been endorsed by Pearl 2009, Hitchcock 2016, and others. I will discuss three problems with this proposal and suggest that fixing them leads us back to more or less the decision theory of Lewis 1981 and Skyrms 1982.
What makes the Sleeping Beauty problem non-trivial is Beauty's potential memory loss on Monday night. In my view, this means that Sleeping Beauty should be modeled as a case of potential epistemic fission: if the coin lands tails, any update Beauty makes to her beliefs in the transition from Sunday to Monday will also fix her beliefs on Tuesday, and so the Sunday state effectively has two epistemic successors, one on Monday one on Tuesday. All accounts of epistemic fission that I'm aware of then entail halfing.
Decision theory comes in many flavours. One of the most important but least discussed divisions concerns the individuation of outcomes. There are basically two camps. One side -- dominant in economics, psychology, and social science -- holds that in a well-defined decision problem, the outcomes are exhausted by a restricted list of features: in the most extreme version, by the amount of money the agent receives as the result of the relevant choice. In less extreme versions, we may also consider the agent's social status or her overall well-being. But we are not allowed to consider non-local features of an outcome such as the act that brought it about, the state under which it was chosen, or the alternative acts available at the time. This doctrine doesn't have a name. Let's call it localism (or utility localism).
Necessitarian and dispositionalist accounts of laws of nature have a well-known problem with "global" laws like the conservation of energy, for these laws don't seem to arise from the dispositions of individual objects, nor from necessary connections between fundamental properties. It is less well-known that a similar, and arguably more serious, problem arises for dynamical laws in general, including Newton's second law, the Schrödinger equation, and any other law that allows one to predict the future from the present.
Decision theory says that faced with a number of options, one should choose an option that maximizes expected utility. It does not say that before making one's choice, one should calculate and compare the expected utility of each option. In fact, if calculations are costly, decision theory seems to say that one should never calculate expected utilities.
Informally, the argument goes as follows. Suppose an agent faces a choice between a number of straight options (going left, going right, taking an umbrella, etc.), as well as the option of calculating the expected utility of all straight options and then executing whichever straight option was found to have greatest expected utility. Now this option (whichever it is) could also be taken directly. And if calculations are costly, taking the option directly has greater expected utility than taking it as a result of the calculation.
I'm currently teaching a course on decision theory. Today we discussed chapter 2 of Jim Joyce's Foundations of Causal Decision Theory, which is excellent. But there's one part I don't really get.
Joyce mentions that Savage identifies acts with functions from states to outcomes, and that Jeffrey once suggested representing such functions as conjunctions of material conditionals: for example, if an act maps S1 to O1 and S2 to O2, the corresponding proposition would be (S1 → O1) & (S2 → O2). According to Joyce, this conception of acts "cannot be correct" (p.62). That's the part I don't really get.
A lot of what I do in philosophy is develop models: models of rational choice, of belief update, of semantics, of communication, etc. Such models are supposed to shed light on real-world phenomena, but the connection between model and reality is not completely straightforward.
For example, consider decision theory as a descriptive model of real people's choices. It may seem straightforward what this model predicts and therefore how it can be tested: it predicts that people always maximize expected utility. But what are the probabilities and utilities that define expected utility? It is no part of standard decision theory that an agent's probabilities and utilities conform in a certain way to their publicly stated goals and opinions. Assuming such a link is one way of connecting the decision-theoretic model with real agents and their choices, but it is not the only (and in my view not the most fruitful) way. A similar question arises for the agent's options. Decision theory simply assumes that a range of "acts" are available to the agent. But what should count as an act in a real-world situation: a type of overt behaviour, or a type of intention? And what makes an act available? Decision theory doesn't answer these questions.
There has been a lively debate in recent years about the relationship between graded belief and ungraded belief. The debate presupposes something we should regard with suspicion: that there is such a thing as ungraded belief.
Compare earthquakes. I'm not an expert on earthquakes, but I know that they vary in strength. How exactly to measure an earthquake's strength is to some extent a matter of convention: we could have used a non-logarithmic scale; we could have counted duration as an aspect of strength, and so on. So when we say that an earthquake has magnitude 6.4, we characterize a central aspect of an earthquake's strength by locating it on a conventional scale.
Philosophers (and linguists) often appeal to judgments about the validity of general principles or arguments. For example, they judge that if C entails D, then 'if A then C' entails 'if A then D'; that 'it is not the case that it will be that P' is equivalent to 'it will be the case that not P'; that the principles of S5 are valid for metaphysical modality; that 'there could have been some person x such that actually x sits and actually x doesn't sit' is an unsatisfiable contradiction; and so on. In my view, such judgments are almost worthless: they carry very little evidential weight.
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