Itzhak Gilboa is one of my favorite economists. His book with David Schmeidler, A Theory of Case-Based Decisions (Cambridge: Cambridge University Press, 2001) is path breaking in amending the traditional Savage "small world" model of rational choice to be more realistic and useful. Rational Choice aims to present rational choice theory for newcomers without social scientific, philosophical, or mathematical expertise. Despite is diminutive size, the book ends up as a broadly accurate description of the current state of rational choice theory.
Gilboa is well aware of the limitations of standard the rational actor model, and makes no attempt in this book to go beyond this model (despite his own brilliant work on "case-based choice theory"). Rather, he considers the model as a "paradigm" rather than a "theory." The paradigm gives us a useful way of looking at the world, although by no means the only pertinent way. Gilboa urges the reader to add rational choice theory to his repertoire of tools used to assess social policy.
Rational Choice claims to be a "rigorous, concise, and nontechnical introduction to some of the fundamental insights of rational choice theory." (from the cover) Rational choice theory is well-suited for a concise nontechnical treatment, which this book is, but far from being rigorous, Gilboa is often simply incorrect, and rarely is convincing. The book appears to be directed to the layman with innate but inchoate prejudices against rational choice theory, but I doubt that such an individual will find this volume convincing.
Most opposition to rational choice theory that I have encountered, even when offered by professional behavioral scientists, is in fact couched in vague often even and ignorant terms. But there is a real critique of the theory. Gilboa simply doesn't locate it. For instance, Chapter 8 on Free Markets presents a very realistic objection to free markets and globalization in which the defender of market equilibrium, using the First Welfare Theorem, is completely incapable of even making a dent in the critics' arguments, and storms off in an angry huff. Gilboa's problem is twofold. First, the only plausible argument for free markets is dynamic and based on the innovative implications of competition and not on the First Welfare Theorem. In fact, as Arnold Harberger showed many years ago, the welfare losses of protection are generally quite small. Second, this issue has nothing to do with rational choice. Free markets have some desirable static allocational properties if agents make choices that are consistent with their welfare. Rational choice, as has been evident at least since Gary Becker's study of addiction and contemporary models of obesity, has no clear connection to making choices consonant with personal welfare.
Gilboa offers an indefensible definition of rationality. Spurning the traditional consistency definition of Savage (1954) and others, Gilboa offers the following: "a mode of behavior is rational for a given person if this person feels comfortable with it, and is not embarrassed by it even when it is analyzed for him." (p.5) The problem with this definition is that it has no analytical implications at all, and it deals with normative choice theory, not behavioral. If we add some ancillary assumptions, such as "a person will be embarrassed to find that his choices are inconsistent," then we restore the traditional definition of rationality. Why then this roundabout definition, couched in terms of the persuasive power of the author and presuming a high level of cognitive functioning of the rational agent? Gilboa argues that "An irrational mode of behavior is one that I can hope to change by talking to the decision maker, by explaining the theory to him, and so forth." (p. 5) Bringing the authors motives into the analysis, it appears, only confuses the issue even more. In the rest of the book, Gilboa does stick to the traditional definition of rationality, but he never explains why.
In Chapter 2, Gilboa tries to explain why a young lady, Ann, ignorant of rational choice theory, could improve her ability to solve her problem of choosing among boyfriends by applying rational choice theory. He quite fails to convince. Indeed, I cannot imagine why knowledge of rational choice theory could help Ann make such a decision.
Gilboa also treats very breezily some issues that merit lengthy argumentation and many examples. For instance, he treats base rate bias and conditional probabilities with a single example and biased samples with another single simple example. There is little chance a novice with appreciate the importance of these issues. They are easily explained with simple arithmentic and elementary probability theory.
Perhaps the most egregious failure of this book is to deal in any consistent way with empirical studies of human behavior in the context of strategic interaction. Instead, Gilboa gives off-hand observations about daily life that insult the critical faculties of the reader. Indeed, Gilboa's mode of argumentation makes understanding empirical studies conceptually impossible. For instance, it is well known that many individuals prefer to cooperate in a prisoner's dilemma, provided that they have some assurance that their partners will cooperate as well. Indeed, this finding is one of the more striking regularities in behavioral game theory. For Gilboa, however, the game payoffs should "incorporate any relevant payoffs---material, psychological, sociological and so forth." (p. 96) By not defining the game by its material payoffs, Gilboa assures that no experimentation at all is possible. One cannot set up a prisoner's dilemma and investigate the behavior of the subjects, because by definition, rational subjects must defect. If they do not, then the game is not a prisoner's dilemma. Indeed, different players may be playing altogether different games according to Gilboa's methodology! By constrast with Gilboa, experimental methodology requires defining a game by its material payoffs, and investigating the subjects' possible non-self-regarding preferences by studying the way they play in a common, objective, frame of reference.
Similarly, Gilboa explains the public goods game without reference to the empirical literature on the subject. I find this treatment completely unacceptable. If Gilboa does not know this empirical literature, he should find out about it and transmit it to his readers, if he pretends to be rigorous. Or perhaps he believes that the evidence not a part of rigorous analysis. If so, he is mistaken.
Gilboa's discussion of altruism is also breezy, perfunctory, and quite lacking in rigor or understanding of the literature. For instance, he assumes without discussion that (p. 98) that altruistic giving involves having the welfare of the recipient in one's utility function, showing no recognition of the work of Andreoni and others on warm-glow altruism, or of other conceptions of other-regarding behavior.
Spurning the considerable literature on group size and cooperation in the public goods game, Gilboa asserts that cooperation is more likely in small groups, giving the example of driving in the suburbs as opposed to the city. This sort of reasoning is quite unscientific, and likely leads the reader to value unscientific reasoning.
Gilboa attempts to present the notion of Nash equilibrium and critique it in just two or three pages. This does not give the concept its due. At least twenty pages are required to draw out the implications of the Nash criterion with any rigor, and this can be done with only elementary arithmetic and some logic. He then introduces rationalizability without a single example, and common knowledge of rationality without any critical treatment. Another twenty pages of non-mathematical yet rigorous analysis could clarify these concepts, but they are not present in this book. He similarly mentions "Nash equilibrium in beliefs" in one short paragraph, the chance of being understood by the layman being zero. He similarly presents backward induction in one page, with no examples, and no critical commentary.
In sum, Gilboa appears incapable of distinguishing between nonmathematical analysis and careless analysis, perhaps on the grounds that readers who do not understand mathematical argumentation are necessarily careless thinkers. They are not. This book is full of careless and perfunctory analysis and might appeal to careless thinkers. Few others will approve.