The basic principle of decision making based on substantive rationality is very simple: one seeks to maximize expected utility. This principle has led to a body of mathematics that accommodates ways to rank-order expectations and to search or to solve for the option (or options) that meet the optimality criteria. The major mathematical components of this approach are utility theory, probability theory, and calculus.

The basic principle of decision making based on intrinsic rationality is also very simple: one seeks acceptable tradeoffs. To be useful, this principle must be supported by a body of mathematics that accommodates ways to formulate tradeoffs and to identify the options that meet the satisficing criteria. This chapter introduces such a mathematical structure. It also is composed of utility theory, probability theory, and calculus, but with some important differences in the structure and the application of these components (Stirling and Morrell, 1991; Stirling, 1993; Stirling, 1994; Stirling et al., 1996a; Stirling et al., 1996c; Stirling et al., 1996b; Goodrich et al., 1999; Stirling and Goodrich, 1999a; Goodrich et al., 2000).