Can quantum theory provide new answers to puzzling results from decision research that have resisted formal explanations so far? This chapter presents several new contributions that quantum theory provides to decision research. However, in order to locate where quantum theory can make an important new contribution, we first need to provide some necessary background on decision theory and what has already been accomplished.

Decision science is a highly developed field that has produced a variety of sophisticated mathematical theories (Gilboa, 2009; Wakker, 2010). Some of these theories are rational theories, which prescribe optimal ways to make decisions. Others are psychological theories that describe the way people actually make decisions.

One of the most important rational decision theories is von Neumannn and Morgenstern's expected utility (EU) theory (von Neumann & Morgenstern, 1944). Expected utility theory is designed for decisions under risk; that is, a choice among actions defined as an objective probability distribution over possible payoffs. An important extension of (EU) theory is Savage's (1954) subjective expected utility (SEU) theory. This extends utility theory to decisions under uncertainty; that is, a choice among actions defined as functions that map un-certain events into payoffs, and the events may not have objective probabilities. A more general theory designed for decisions under both uncertainty and risk was presented by Anscombe and Aumann (1963). All of these theories are rational, in the sense that they are based on a small set of compelling axioms and the prescribed action logically follows from the axioms.