General remarks on the study of preference and choice
There is a huge theoretical literature on preference and choice, with a corresponding large literature on testing theories. In this chapter we focus almost entirely on theoretical work. In this section we review some empirical applications that motivate some of our theoretical primitives, such as the “sample spaces” for which probabilistic models are designed. In later sections, we provide references to relevant empirical work.
Recent important books, review articles, and handbooks, with a theoretical emphasis, include Barberá et al. (1999, 2004, 2013); Gilboa (2009); Luce (2000); and Wakker (2010). We focus on the past 15 years in this chapter and, for a significant part, restrict the content to general multiattribute options. While we provide some in-depth details for choice under uncertainty, we do not go into specialized models of intertemporal or sequential choice. Also, to keep the bibliography manageable, we often cite only one or two most relevant articles on a topic.
Historically, research on preference and choice has placed an emphasis on deterministic representations, most notably, algebraic models of preference, utility, and choice. A notorious challenge, for over 50 years, has been the question of adequate representation for data showing different choices in repeated presentations of the same task, both within a person and across decision makers.
This formal modeling challenge is sometimes associated with Duncan Luce, whose 1959 choice axiom was a major milestone in probabilistic characterizations of utility.Many other leading scholars have also studied and discussed ways to generalize algebraic models into probability models (see Blavatskyy and Pogrebna, 2010; Stott, 2006; Wilcox, 2008, and their citations). We will emphasize probabilistic representations of preference, utility and choice, and we will consider deterministic representations as the special case where all probability mass is concentrated on a single preference, a single utility function, or a single way of making a choice, and choice based on such a deterministic representation is errorfree. The probabilistic generalizations we consider are based either on the premise that preferences or utilities are deterministic but responses are probabilistic (e.g., due to probabilistic error), or on the premise that preferences are probabilistic and responses are deterministic.
The focus is on theory, with data and model fitting introduced only when such is intimately connected to the theory.