The framework of Solomonoff prediction assigns prior probability to hypotheses inversely proportional to their Kolmogorov complexity. There are two well-known problems. First, the Solomonoff prior is relative to a choice of Universal Turing machine. Second, the Solomonoff prior is not computable. However, there are responses to both problems. Different Solomonoff priors converge with more and more data. Further, there are computable approximations to the Solomonoff prior. I argue that there is a tension between these two responses. This is because computable approximations to Solomonoff prediction do not always converge.

We study group decision making with changing preferences as a Markov Decision Process. We are motivated by the increasing prevalence of automated decisionmaking systems when making choices for groups of people over time. Our main contribution is to show how classic representation theorems from social choice theory can be adapted to characterize optimal policies in this dynamic setting. We provide an axiomatic characterization of MDP reward functions that agree with the Utilitarianism social welfare functionals of social choice theory. We also provide discussion of cases when the implementation of social choice-theoretic axioms may fail to lead to long-run optimal outcomes.

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Chancy modus ponens is the following inference scheme: ‘probably φ’, ‘if φ, then ψ’, therefore, ‘probably ψ’ (Yalcin 2010, Moss 2015). I argue that Chancy modus ponens is invalid in general. I further argue that the invalidity of Chancy modus ponens sheds new light on the alleged counterexample to modus ponens presented by McGee (1985). I close by observing that, although Chancy modus ponens is invalid in general, we can recover a restricted sense in which this scheme of inference is valid.

We argue that subjective Bayesians face a dilemma: they must offend against the spirit of their permissivism about rational credence or reject the principle that one should avoid accuracy dominance.