I’ve been thinking about the Dutch Book Argument (DBA) recently. I think the constraints on rational betting preference that underpin the force of the argument are unreasonable. At least they are not always reasonable. I think a better way to think of the argument is as a conditional argument: “Given these rational betting preference conditions, this is how rational degrees of belief should be constrained.” Then you can have a whole series of different DBAs with different betting preference conditions leading to different constraints on credence. It would be interesting to see how one would have to constrain betting preferences in order to have you beliefs behave like upper and lower probabilities or Dempster-Shafer belief functions…
I think this isn’t to undermine the force of the DBA, but to reinforce it. With this wider framework we can understand why people often fail to reason probabilistically. We can understand what aspects of rational betting preference are “non-probabilistic”.
That’s not to say that the DBA isn’t without its flaws. Some elements that concern me are:
- Using betting behaviour as a proxy for belief
- Existence of exactly specific numerical credence (and utility)
- Reasoning as calculating expected utilities
- The idealisations involved in discussing “ideal rational agents”: utility maximising, purely self interested, perfect calculating agents…