The sure-thing principle

Abstract

Savage (1954) 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
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 principles 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.

The paper is at
http://www.tau.ac.il/~samet/papers/the-sure-thing-principle.pdf