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1. INTRODUCTION
What constitutes rationality for belief and decision? A variety of domains, from epistemology to economics, from decision theory to decision analysis, standardly look to Classic Bayesianism for the answer. Founded on the idea that beliefs admit gradations of strength between the extremes of categorical acceptance or rejection of a proposition – Bayesians often speak of grades of uncertainty, degrees of belief, subjective probability or credences – this position can be summarized in three intertwined tenets, concerning belief, decision making and learning respectively. This paper focuses on the first two:
1. A thesis about rational belief: Gradations of belief strength are represented by the assignment of a single number (between 0 to 1) to each proposition or event. These numbers satisfy the laws of probability.
2. A thesis about rational decision: The chosen action in any decision is that which maximizes the expected utility or desirability on the basis of the agent’s graded beliefs.
Bayesianism owes its status as the benchmark account of rational belief and decision making largely to its purported coherence with normative intuitions. Some justify the expected utility rule as directly capturing or following from some normatively appealing pre-formal intuition or principle concerning how choices should be made; Weirich (2001: Ch 3), for instance, purports to derive it directly from a ‘principle of pros and cons’. A more popular route defends the account on the basis of the normative plausibility of its implications for the choices that are made. Dutch Book arguments are of this sort: by purportedly showing that only those with probabilistic beliefs will never accept a set of bets yielding a sure loss (or ‘Dutch Book’) they harness the spontaneous normative attractiveness of this behavioural consequence in support of the Bayesian position (see for example de Finetti 1937; Hájek 2008). The axiomatizations common in economic decision theory can be put to similar use: they establish a set of properties of preferences – the ‘axioms’ – that characterize decision makers who can be represented as adhering to the Bayesian tenets, and hence allow one to argue for the latter by appealing to the normative intuitiveness of the former (Ramsey 1931; Savage 1954; Gilboa 2009; Gilboa et al. 2010; Cozic and Hill 2015).
Another important advantage of...