Practical foundations for probability: Prediction methods and calibration

Although probabilistic statements are ubiquitous, probability is still poorly understood. This shows itself, for example, in the mere stipulation of policies like expected utility maximisation and in disagreements about the correct interpretation of probability. In this work, we provide an account of probabilistic predictions that explains when, how, and why they can be useful for decision-making. We demonstrate that a calibration criterion on finite sets of predictions allows one to anticipate the distribution of utilities that a given policy will yield. Based on this, we specify assumptions under which expected utility maximisation is a sensible decision criterion. We also introduce the notion of prediction methods, highlighting the dependence on schemes of abstraction, and argue that all probabilities are outputs of such prediction methods. This helps explain how the calibration criterion can be satisfied and shows that also supposedly objective probabilities are model-dependent. We compare our account of probability with conventional interpretations and show that it recovers key intuitions behind the latter. We, thus, provide a general account of what probabilities are and how they can enable successful decision-making under uncertainty.