The sure-thing principle and independence of irrelevant knowledge Dov Samet The Faculty of Management, Tel Aviv University ∗ July 16, 2008 Abstract Savage (1954) introduced the sure-thing principle in terms of the de- pendence of decisions on knowledge, but gave up on formalizing it in epistemic terms for lack of a formal definition of knowledge. Using simple models of knowledge, we examine the sure-thing principle, presenting two ways to capture it. One is in terms of the union of future events, for which we reserve the original name—the sure-thing principle ; the other is in terms of the intersection of kens —bodies of agents’ knowledge—which we call independence of irrelevant knowledge. We show that the two prin- ciples are equivalent and that the only property of knowledge required for this equivalence is the axiom of truth—the requirement that whatever is known is true. We present a symmetric version of the independence of irrelevant knowledge which is equivalent to the impossibility of agreeing to disagree on the decision made by agents, namely the impossibility of agents making different decisions being common knowledge 1 Introduction 1.1 An example of the sure-thing principle The sure-thing principle (STP) was introduced by Savage (1954) using the fol- lowing story. A businessman contemplates buying a certain piece of property. He considers the outcome of the next presidential election relevant. So, to clarify the matter to himself, he asks whether he would buy if he knew that the Democratic candidate were going to win, and decides that he would. Similarly, he considers whether he would buy if he ∗ Currently on leave at ILLC, University of Amsterdam and CWI, Amsterdam, The Nether- lands. 1