On the Expected Utility Objection to the Dutch Book Argument for Probabilism*

Abstract

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden, 2013; Wroński & Godziszewski, 2017; Wroński, 2018)-I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument.

Modus Ponens and the Logic of Decision

“…"Suppose your credence in X is p. Consider a $S bet on X [that pays $S if X and $0 otherwise]... You are rationally required to pay $x for this bet, if x < pS ." (Pettigrew 2019: 4) (cf. also Christensen 2004Hedden 2013) Thus, for example, a probabilistically incoherent agent who assigns X credence .6 and Y credence .6 (when Y is logically equivalent to ¬X) is required to pay $.55 for a bet that pays $1 if X and to pay $.55 for a bet that pays $1 if Y.…”

Nonclassical Probability, Convex Hulls, and Dutch Books

“…If there are n truth values, we could equivalently be talking either about B or about n functions from Sent L to [0, 1]; for example, in the case where TV has three elementswhatever they areit might be convenient to speak about a credence function by referring to the indexed set of functions {B 1 (⋅), B 1/2 (⋅), B 0 (⋅)}. 28 While the ideas here are meant to be general, so that a variety of nonclassical logics and corresponding notions of credence can be considered, all examples illustrating our 25 This is problematic on its own; see Hedden (2013), Godziszewski (2017), andPettigrew (2021). (For starters, when arguing for probabilism it is a mistake to assume that B(¬A) = 1 − B(A); this should be a conclusion, not an assumption.)…”

Towards the Inevitability of Non-Classical Probability

“…After settling on (i), (ii) is fairly uncontroversial: if all we care about is accuracy, and cr ′ is more accurate than cr no matter what, then there's no reason why we should hold the latter instead of the former. On the other hand, Joyce's assumptions on (iii) 3 The standard references are Pettigrew (2011Pettigrew ( , 2016, in which it is argued that accuracy is the fundamental epistemic virtue on the basis that all others can be derived from it. This position is known as veritism.…”

“…Avoiding accuracy-domination does not require credences to be probabilistic; instead, Lindley argues, it merely requires that they can be transformed into probabilistic functions by a canonical transform. 3 The standard references are Pettigrew [13,14], in which it is argued that accuracy is the fundamental epistemic virtue on the basis that all others can be derived from it. This position is known as veritism.…”