Reading Evidence, Decision and Causality

How odd. I'm in the office. I'm not terribly exhausted. I have some time to read and think and write. Where do I start?

Here's a book that I've long wanted to read carefully, but never got around to: Arif Ahmed's Evidence, Decision and Causality (Ahmed (2014)). I'll work my way through it, and post my reactions. This first post covers the preface, the introduction, and the first two chapters.

The book is an extended defence of Evidential Decision Theory. When I read a text with whose conclusion I disagree, I often find that the discussion already starts off on the wrong foot, with dubious presuppositions about the topic and how to approach it. Not so here. I'm largely on board with how Arif frames the disagreement between Evidential Decision Theory (EDT) and Causal Decision Theory (CDT). I like his broader philosophical outlook – his positivism, his distrust of metaphysics, his conviction that decision-makers should see themselves as part of the natural world. It should to be interesting to see where we'll end up disagreeing.

One difference in perspective becomes clear at the very start of the book.

Arif assumes that friends of CDT believe in a metaphysically special relation of causation, which, they think, should guide our practical deliberation: we should try to act in a way that causes or produces good outcomes. Arif doesn't believe in any such relation. "Causality", he says, "is a pointless superstition." (This is the first sentence in the preface.) Even if there were such a relation, he thinks it would be mysterious why it should play the suggested role in practical deliberation.

I share these concerns about views that posit causation – or counterfactuals, or other notions in the same ballpark – as metaphysically primitive. I, too, doubt that these posits exist, and I find it mysterious how they could play the roles they are assumed to play.

But I don't think CDT is committed to any particular metaphysics of causation. Many prominent formulations of CDT don't explicitly involve causation at all. My favourite formulation instead appeals to a notion of subjunctive supposition. It says that when we deliberate about whether to do A or B, we should consider what would (or might, or is likely to) be the case if we were to choose A, and what would (or might, etc.) be the case if we were to choose B.

How do we evaluate a subjunctive supposition? That's a difficult question. An attractive idea is that we consider what happens at worlds that are in certain respects much like (what we believe might be) the actual world but where, somehow, the supposed choice takes place. In what respects should the relevant worlds be like the actual world? To a first approximation, they should match the actual world with respect to everything that's causally independent of the relevant choice. So here we may find a causal notion. But at this point, it only shows up in a rough gloss of a tentative analysis of subjunctive supposition. I'm not convinced that causal notions – let alone any supposedly primitive causal notions – will figure in a more adequate analysis.

As I don't think CDT is committed to a special metaphysics, I am not moved by the metaphysical considerations Arif mentions in the introduction. Fortunately, the rest of the book doesn't seem to rest on these considerations. It mostly rests on particular cases in which CDT and EDT appear to give different verdicts.

Chapter 1 introduces Savage's decision theory, and points out that both CDT and EDT can be seen as developments of Savage's account. There are few original points here, but the presentation is nice.

Savage's theory is based on a quasi-behaviourist attitude towards belief and desire. Unlike most contemporary decision theorists within philosophy, Arif is sympathetic to this approach. Beliefs and desires, he suggests, are best understood not as internal states that cause actions, but ass "a complicated amalgam of preferences", "not identifiable [to the agent] prior to the formation of any practical dispositions" (pp.25,28).

Yet, Arif argues, this attractive picture can't be maintained. The problem is that Savage's theory only yields sensible results if the agent believes that the "states" are independent of the "acts", and these beliefs can't be determined by the agent's preferences. (p.33f.)

This problem was new to me. It seems to arise only on an evidential development of Savage's theory. As Arif mentions in footnote 16, on a causal conception, one could simply stipulate that the states in a well-defined decision-problem should have a particular form (say, that of the "K-partitions" from Lewis (1981)). Arif points out that most of the Savage-style "acts" in the resulting decision problem might then become unintelligible. That's true. And that's a further problem for Savage's approach – a problem that also arises in the evidential development. (For a simple example, suppose an "outcome" involves having chosen a certain act A. Then how should we evaluate a hypothetical act B, distinct from A, that has this same outcome?)

Arif's response to the failure of Savage's behaviourism, described in chapter 2, is to take as primitive a preference relation over arbitrary propositions. The relation is assumed to satisfy the Jeffrey-Bolker axioms. Since this doesn't allow deriving a unique credence function, we also take as primitive an "equal confidence" relation over propositions.

In that framework, EDT can then be expressed very neatly. It says that an agent should choose an option that is (weakly) preferred to all others.

The alternative, CDT, is spelled out roughly a la Lewis (1981). That is, expected utilities are calculated as in Savage, but the "states" in a decision problem are fixed to specify the conditional chance of each outcome given each option. Not much is said about how the relevant notion of conditional chance should be understood. Arif assumes that this is an essentially causal notion.

Arif then complains that implementing CDT is "more demanding" then implementing EDT, because the hypotheses about conditional chance will often be extremely fine-grained. Even partition-invariant formulations of CDT (such as that of Joyce (1999)) are said to face the same problem, since they also rely on a specification of utilities for extremely fine-grained propositions.

OK. But the reason why EDT comes out much simpler is that we started with an "evidential" preference relation that compares propositions in terms of news value. We could instead have started with a "causal" preference relation (as in Joyce (1999)) that compares propositions in terms of how good it would be if they were true. (This relation would not satisfy the Jeffrey-Bolker axioms, but a different set of axioms.) On this bases, CDT could be formulated very neatly, and computing evidential expected utilities would require first computing the probability of very fine-grained propositions. It's a tie.

That said, no doubt EDT is conceptually simpler than CDT, and that's a point in its favour.

Overall, these two chapters are a decent exposition of CDT and EDT, and of how they relate to Savage's earlier theory. Many readers would probably object to Arif's quasi-behaviourist approach to belief and desire. But as far as I can tell this won't be assumed in later chapters.

Ahmed, Arif. 2014. Evidence, Decision and Causality. Cambridge University Press.
Joyce, James. 1999. The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.
Lewis, David. 1981. “Causal Decision Theory.” Australasian Journal of Philosophy 59: 5–30.


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