This appendix uses parts of Wakker (1989a, Ch. 1). Throughout this book we adopt the revealed-preference paradigm: A decision maker chooses the most preferred prospect from a set of available prospects. Then, besides the descriptions of the prospects (that can be general choice options here), the only observable primitives are assumed to be those choices. Utilities, subjective probabilities, and other concepts exclusively obtain their empirical meaning from their implications for the choices made.

In most practical situations there are more than two prospects to choose from. Revealed-preference theory examines when such general choice situations can be represented by preferences – binary choices – after all (Chipman et al. 1971; Houthakker 1950; Mas-Colell, Whinston, & Green 1995 §1.D). Because all of the main text has assumed that optimal choices are fully specified by preferences, this appendix shows how the preference theories in this book are relevant for general decisions.

This appendix assumes a general choice function, defined formally later, as the empirical primitive, rather than binary preference. Binary preference now is the theoretical construct used to model the empirical primitive. Thus, this appendix gives a behavioral foundation for binary preference, justifying its use throughout the book. The elicitation method now does not derive other parameters from binary preference, as this happened in the main text, but it derives binary preference from the choice function. Hence, the term revealed preference has sometimes been used to designate this particular version of the elicitation method, initiated by Samuelson (1938).