Choice with Indexed Alternatives: a Theoretical and Experimental Analysis

In the last forty years, a considerable amount of experimental research in both psychology and economics has reported various violations of the axioms of classical choice theory, but only recently has axiomatic theory started to take into account this empirical evidence. In particular, the recent evidence collected by the new approach of neuroeconomics and the rapid growth of new teorie have triggered a methodological debate about whether and how these sources of new empirical data and psychological insights should be used in economics (Caplin and Schotter, 2008). While some authors suggest to dismiss classical revealed preference analysis arguing that the presence of systematic biases between what people like and what people choose impair the possibility to reveal something by simply observing choices (K¨oszegi and Rabin, 2008), others remain skeptical about extending the classical model to include additional components that cannot be inferred from choice data (Gul and Pesendorfer, 2008). A third group of authors proposes to use the new evidence combined with standard choice–theoretic tools to build economic models that are both more realistic and choice–based (Caplin, 2008; Rubinstein and Salant, 2008). The present work is in this spirit: on one hand it builds on empirical evidence and psychological literature on salience, bandwagon and snob effects, and heuristic behaviour; on the other hand, it adopts a choice–theoretic approach to embed these phenomena into axiomatic models. The first chapter of the thesis covers the recent methodological debate concerning classical decision theory. It briefly points out how economic theory has developed a coherent and organic framework that links together choices, utility, and preference by means of important formal results, and how some of the implicit difficulties regarding the psychological aspects have been neglected. In particular, the chapter discusses the critical assumption that choices depend only on the set of available alternatives and presents the relevant psychological literature and experimental evidence about the effect of alleged irrelevant aspects on choices, i.e., ancillary conditions (Bernheim and Rangel, 2009, p. 55). The second chapter proposes an axiomatic model where choice behaviour of the decision maker is influenced by ancillary conditions. Specifically, the present thesis extends the concept of choices with frames proposed by Bernheim and Rangel (2008, 2009) and by Salant and Rubinstein (2008) according to which choices do not simply depend upon the set of available alternatives, but also upon additional components called frames. The present work defines the abstract concept of frame as a vector of indexes representing a psychological measure that agents attach to each alternative. Choices are then conditioned to the indexes attached to the alternatives. This chapter shows that, if the conditional choice behaviour satisfies two intuitively appealing properties—namely Monotonicity and Conditional IIA—, then the observable part of choice behaviour, i.e., the unconditional choices, can be interpreted as resulting from the maximisation of a preference relation. The chapter discusses also some welfare considerations regarding the choice model and proposes some interpretations of the indexes. The third chapter considers a narrower interpretation of the indexes—each index represents the number of people in a group that choose each alternative—and discusses the properties an extended choice function should satisfy in order to capture the behavioural implications of the “DoWhat The Majority Do” heuristic (Gigerenzer, 2004). This heuristic prescribes that, whenever the choice task is too difficult, the consequences of the alternatives are too complex to evaluate, or the subject is unsure about what to choose, he simply looks at what the majority of his peers does and then engages in the same behaviour. The chapter axiomatises the contents of the “Do What The Majority Do” heuristic by using the monotoni city axiom introduced in chapter 2 together with a maximality axiom, and then shows that an equilibrium is reached if choices satisfy maximality and monotonicity. The fourth chapter presents an experimental test of the two axioms proposed in the third chapter. The test of the axioms is performed using sets of lotteries and groups of 7 people. Participants are asked to choose repeatedly from the same set of lotteries and, after each choice, they are informed about the number of people choosing each of the alternatives. The reaction to changes in the indexes—i.e., to the choices of the members of the group—is thus recorded and the robustness of the axioms is tested. Even though the results support the idea that choices are affected by what the others members of the group do, there is mixed evidence regarding the empirical validity of the two axioms. While strong support in favour of monotonicity is found, there is no clear cut evidence in support of maximality