The Sure-Thing Principle in Epistemic Terms

Abstract: Savage introduced the sure-thing principle in terms of the dependence of decisions on knowledge, but gave up on formalizing it in epistemic terms for lack of a formal definition of knowledge. Using a standard model of knowledge, the partition model, we examine the sure-thing principle, presenting two ways to capture it. One is in terms of knowledge operators, which we call the principle of follow the knowledgeable; the other is in terms of kens – bodies of agents’ knowledge – which we call independence of irrelevant knowledge. We show that the two principles are equivalent. We present a stronger version of the independence of irrelevant knowledge and show that it is equivalent to the impossibility of agreeing to disagree on the decision made by agents, namely the impossibility of different decisions made by agents being common knowledge.