Rationality and indeterminate probabilities

Introduction What is your degree of belief that the Democrats will win the next presidential election in the USA? If you report a sharp number, we will question you further. For example, if you report a credence of 0.6, we will ask whether you really mean 0.6000..., sharp to infinitely many decimal places. If you are anything like us, your credence is sharp only up to one or two decimal places. And in that case, you are not an ideal Bayesian agent. For such an agent assigns perfectly sharp credences to all propositions. Some Bayesians may nevertheless let you into their fold, more or less grudgingly. For they are prepared to countenance indeterminate credences—just how grudgingly will vary from one Bayesian to another. Jeffrey (1992), for example, is quite prepared to give Bayesianism ―a human face‖, and he believes that human credences may be more realistically modelled as a set of probability functions. Still, grudging or not, it seems to be something of a concession: his preferred model of an ideally rational agent portrays her as having a single probability function. In this paper, we will argue that indeterminate probabilities are not only rationally permissible, but they may even be rationally required. We follow Levi‘s (2000)