Introduction to Choice TheoryJonathan Levin and Paul Milgrom∗September 20041 Individual Decision-MakingIndividual decision-making forms the basis for nearly all of microeconomic analysis.These notes outline the standard economic model of rational choice in decision-making. In the standard view, rational choice is defined to mean the process ofdetermining what options are available and then choosing the most preferred oneaccording to some consistent criterion. In a certain sense, this rational choicemodel is already an optimization-based approach. We will find that by addingone empirically unrestrictive assumption, the problem of rational choice can berepresented as one of maximizing a real-valued utility function.The utility maximization approac h grew out of a remarkable intellectual con-vergence that began during the 19th century. On one hand, utilitarian philosopherswere seeking an objective criterion for a science of government. If policies were tobe decided based on attaining the “greatest good for the greatest number,” theywould need to find a utility index that could measure of how beneficial differentpolicies w ere to different people. On the other hand, thinkers following AdamSmith were trying to refine his ideas about how an economic system based onindividual self-interest would work. Perhaps that project, too, could be advancedby developing an index of self-interest, assessing how beneficial various outcomes∗These notes are an evolving, collaborative product. The first version was by Antonio Rangelin Fall 2000. Those original notes we re edited and expanded b y Jon Levin in Fall 2001 and 2004,and by Paul Milgrom in Fall 2002 and 2003.1are to any individual person. Some of the greatest thinkers of the era were bothphilosophers and economists.Could the utilitarian and economic approach es be combined? That questionsuggests several others. How can we tell if the Smithian model of choice is right,that is, that individuals make choices in their own interests? What does that mean,precisely? How can we use data to tell whether the proposition is true? What areall the empirical implications of rational choice? What kind of data do we needto make the test? Even if the Smithian model is true, can the utility function weneed for policy-making be recovered from choice data? If we can recover utilities,is simply adding up utilities really the best way to use that information for publicdecisions? What is the best way to use that information?The utility-maximization approac h to choice has several characteristics thathelp account for its long and continuing dominance in economic analysis. First,from its earliest development, it has been deeply attached to principles of govern-ment policy making. The original utilitarian program proved to be too ambitious,but the idea that welfare criteria could be derived from choice data has provedto be workable in practice. Moreover, because this approach incorporates theprinciple that people’s own choices should determine the government’s welfare cri-terion, it is well-aligned with modern democratic values. Second, many of thecomparative statics predictions of the c h oice theory – the qualitative predictionsconcerningthewaysinwhichchoiceschangeaspeople’senvironmentschange–tend to be confirmed in empirical studies. Third, the optimization approach (in-cluding utility maximization and profit maximization) has a spectacularly widescope. It has been used to analyze not only personal and household choices abouttraditional economic matters like consumption and savings, but also choices abouteducation, marriage, child-bearing, migration, crime and so on, as well as businessdecisions about output, investment, hiring, entry, exit, etc. Fourth, the optimiza-tion approach provides a compact theory that makes empirical predictions from arelatively sparse model of the choice problem – just a description of the c hooser’sobjectives and constraints. In contrast, for example, psychological theories (withstrong support from laboratory experiments) predict that many choices dependsystematically on a much wider array of factors, such as the way information is2presented to the subjects, the noise level in the laboratory and other variables thatmight influence the subject’s psycholo gical state.Despite the attractions of the rational choice approach, its empirical failings ineconomics and psychology experiments have promoted an intense interest in newapproaches. A wide range of alternative models have been advocated. Learningmodels, in which individuals make choices like those that have w orked well forthem in the past, have attracted particular attention from economic theorists andexperimenters. Bounded rationality models in which decision makers adopt rulesthat evolve slo wly have had some empirical successes. For example, a model inwhich department stores use standard mark-ups to set retail prices appears to givea better account of those prices than does a simple profit maximization model,according to which mark-ups vary sensitively according to price elasticities. Othermodels assume that people seek acceptance by imitating their peers, rely on in-tuition on heuristics, or make choices that are heavily influenced b y their currentemotional state. Recent research try to identify parts of the brain involved indecision-making and model how brain processes affect decisions. Still others giveup on modeling c hoice mechanisms at all and simply concentrate on measuringand describing what people choose.Although these various alternatives appear to ha ve advantages for some pur-poses, in this class we will focus on the decidedly useful and still-dominant modelof rational choice.2 Preferences and ChoiceRational choice theory starts with the idea that individuals have preferences andchooseaccordingtothose. Ourfirst task is to formalize what that means andprecisely what it implies about the pattern of decisions we should observe.Let X be a set of possible choices. In consumer choice models, one migh tspecify that X ⊂ Rn, meaning for instance that there are n different goods (beer,tortilla chips, salsa, etc..) and if x ∈ X,thenx =(x1, ..., xn)specifies quantities ofeach type of good. In general, however, the abstractness of the choice set X allowsenormous flexibility in adapting the model to various applications. Some of the3controversies about the scope of economic theory concern whether the assumptionswe will make belo w to describe