Sven Neth

Suppose we observe many emeralds which are all green. This observation usually provides good evidence that all emeralds are green. However, the emeralds we have observed are also all grue, which means that they are either green and already observed or blue and not yet observed. We usually do not think that our observation provides good evidence that all emeralds are grue. Why? I argue that if we are in the best case for inductive reasoning, we have reason to assign low probability to the hypothesis that all emeralds are grue before seeing any evidence. My argument appeals to random sampling and the observation-independence of green, understood as probabilistic independence of whether emeralds are green and when they are observed.

How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure subjective probability for partly irrational agents.

Is more information always better? Or are there some situations in which more information can make us worse off? Good (1967) argues that expected utility maximizers should always accept more information if the information is cost-free and relevant. But Good's argument presupposes that you are certain you will update by conditionalization. If we relax this assumption and allow agents to be uncertain about updating, these agents can be rationally required to reject free and relevant information. Since there are good reasons to be uncertain about updating, rationality can require you to prefer ignorance.