¹ For succinct discussions of this point see Brennan, Geoffrey, ‘What Might Rationality Fail to Do?’, The Limits of Rationality, ed. Cook, Karen Schweers and Levi, Margaret, Chicago, 1990Google Scholar, and Epstein, Richard, Simple Rules for a Complex World, Cambridge, Mass., 1995Google Scholar.

² Some theorists of rationality have suggested that it may be rational to satisfice -that is, to settle for an adequate amount of good – rather than to maximize. See Simon, Herbert, ‘Rational Choice and the Structure of the Environment’, Economics, Bounded Rationality, and the Cognitive Revolution, ed. Simon, Herbert et al. , Brookfield, Vermont, 1992Google Scholar, and Slote, Michael, Beyond Optimality: An Essay on Rational Choice, Cambridge, Mass., 1989CrossRefGoogle Scholar. The question of whether it is rational to satisfice rather than to optimize raises questions too complex to deal with here. It is likely, however, that the problems of incommensurability and expressivity that are aimed at an optimizing version of consequentialism could also be levelled at a satisficing version of consequentialism.

³ One of which is the actual rationality of the parties to the contract. As a matter of brute psychological fact, human rationality may be defective, inefficient at maximizing. A good summary of work on this empirical issue is Camerer, Colin, ‘Individual Decision Making’, The Handbook of Experimental Economics, ed. Kagel, John H. and Roth, Alvin, Princeton, 1995Google Scholar. Readers may be relieved to know that I do not enter into the vexed question of how rational human beings actually are. The central question behind this paper is the normative one.

⁴ See Dennett, Daniel, Consciousness Explained, Boston, 1991, pp. 437–44Google Scholar, where he applies this term to John Searle's famous ‘Chinese room’ thought experiment.

⁵ These requirements are not exactly von Neumann and Morgenstern's own; rather they are a generalization of the concept vNM utilities worked out by John Harsanyi. See Harsanyi, John, ‘Normative Validity and Meaning of von Neumann-Morgenstern Utilities’, Frontiers of Game Theory, ed. Binmore, Ken, Kirman, Alan, and Tani, Piero, Cambridge, Mass., 1993Google Scholar.

⁶ One significant exception is the decision theorist Anand, Paul, who, in an elegant little book entitled Foundations of Rational Choice under Risk, Oxford, 1993Google Scholar, explicitly argues that one can reasonably reject the axiomatic foundations of modern utility theory. Limits on space do not permit me to reproduce my response to him here. Interested readers should see note 34 to chapter one of my Utilitarianism, Institutions, and Justice, New York, 1997Google Scholar.

⁷ A vNM utility function of course requires that an agent have a preference ordering over states of affairs, but grounds for these preferences need not just be what an agent desires. The ordering may emerge from any account an agent may give of why he makesone choice rather than another, as long as those choices are consistent.

⁸ Raz, Joseph, The Morality of Freedom, Oxford, 1985, pp. 321–68Google Scholar.

⁹ Finnis, John, Fundamentals of Ethics, Oxford, 1987, pp. 86–93Google Scholar.

¹⁰ George, Robert, Making Men Moral, Oxford, 1993, pp. 88–90Google Scholar.

¹¹ George, p. 88.

¹² See Barry, Brian, Political Argument, London, 1965, pp. 3–8Google Scholar.

¹³ John Searle once used a formulation like this in an aside in a lecture on another topic. Actually, in Searle's declaration the amount of money in play is only a dime, but the principle at stake is similar, and indeed the examples could be made structurallyidentical, since there is a sequence of bets with the probability p* of death and otherwise a dime which, if aggregated and played in sequence, would be mathematically equivalent to a lottery with probability p of death with twenty dollars as a prize.

¹⁴ Anand, p. 97.

¹⁵ James Griffin notes the existence of a similar kind of Sorites-like paradox, albeit in a dimension other than continuity. See Griffin, James, Weil-Being: Its Meaning, Measurement, and Moral Importance, Oxford, 1986, p. 87Google Scholar.

¹⁶ They make all sorts of strange errors. For two good readable accounts, see Gilovich, Thomas, How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life, New York, 1991Google Scholar, and Piatelli-Palmarini, Massimo, Inevitable Illusions: How Mis-takes of Reason Rule Our Minds, trans. Piatelli-Palmarini, Massimo and Botsford, Keith, New York, 1994Google Scholar.

¹⁷ For a good introductory discussion of self-deception, see Wright, Robert, The Moral Animal: Evolutionary Psychology and Everyday Life, New York, 1994, ch. 13Google Scholar.

¹⁸ On the phenomenon of ‘dating’ of risks and its consequencesfor public policy, see Fumento, Michael, Science under Siege, New York, 1993, pp. 262fGoogle Scholar.

¹⁹ Griffin, p. 82.

²⁰ See Finnis, John, Natural Law and Natural Rights, Oxford, 1980, pp. 118–25Google Scholar.

²¹ That conflicts between beauty and life may push us to make some hard choices may have meaning in non-stochastic contexts too. Daniel Dennett, in an odd moment of argument which seems to be aimed at incommensurability, but perhaps points in a different direction, put it this way: ‘Which is worth more, a human life or the Mono, Lisa? There aremany who would give up their lives to save the painting from destruction, and many more would sacrifice someone else's life for it, if push came to shove. (Are the guards in the Louvre armed? What steps would they take if necessary?)’ See Dennett, Daniel, Darwin's Dangerous Idea, New York, 1995, p. 513Google Scholar. If there are intelligible, defensible answers to Dennett's questions, then perhaps incommensurability really is not what it is stacked up to be.

²² Raz, pp. 348–50.

²³ See Katz, Leo, ‘Blackmail and Other Forms of Arm-twisting’, University of Pennsylvania Law Review, cxli (1993), 1567CrossRefGoogle Scholar and a similar discussion of greater length in Katz, Leo, Ill-Gotten Gains, Chicago, 1996, pp. 133–96Google Scholar.

²⁴ See Broome, John Weighing Goods, Oxford, 1991, pp. 94–115Google Scholar where he argues that an expected loss of money is not the same as an expected loss of money with regret, as a means of squaring conventional utility theory with Allais's famous paradox.I do not mean to suggest here that his distinguishing outcomes finely is always a mistaken strategy, only that in the case of something like the paradoxes of blackmail and friend-ship distinguishing between states that finely can well lay one open to charges of desperate ad-hocery.

²⁵ Tullock, Gordon, ‘The Welfare Costs of Tariffs, Monopolies, and Theft’, Western Economic Journal, v (1967), 224Google Scholar.

²⁶ Axelrod, Robert, The Evolution of Cooperation, New York, 1984Google Scholar.

²⁷ Smith, John Maynard, Evolution and the Theory of Games, New York, 1973Google Scholar.

²⁸ See Posner, Richard, ‘Blackmail, Privacy, and Freedom of Contract’, University of Pennsylvania Law Review, cxli (1993), 1817CrossRefGoogle Scholar, and Posner, Richard, ‘The Legal Protection of the Face We Present to the World’, Overcoming Law, Cambridge, Mass., 1995Google Scholar.

²⁹ Indeed, so strategic is this intrepid pair that Annina attempts at the end of Act II to extract a payment from Ochs in return for not even attempting any intrigue against him with the ominous hint, ‘Vergessen nicht der Botin, Euer Gnade’. With a descent to an E below the staff on the first syllable ofGna-de, her remark is clearly a threat (which Ochs, to his later sorrow, ignores). See Strauss, Richard, Der Rosenkavalier. Vollständiger Klavier-Auszug mit deutschem Text, Berlin, 1911Google Scholar, republished as Der Rosenkavalier: Vocal Score, New York, 1987, p. 290Google Scholar.

³⁰ Scholars of law and economics offer a different analysis of why blackmail is a crime when the target of blackmail is a criminal, an analysis which turns on the relative efficiency of private versus public law enforcement. See Richard Posner, ‘Blackmail, Privacy and Freedom of Contract’, and Ginsberg, Douglas H. and Schectman, Paul, ‘Blackmail: An Economic Analysis of the Law’, University of Pennsylvania Law Review, cxli (1993), 1849CrossRefGoogle Scholar.

³¹ Anderson, p. 88.

³² Anderson, p. 40.

³³ Ken Binmore, in arguing for what he calls Hobbist psychology, makes a similar point. ‘People presumably feel somehow diminished at the suggestion that they are “no better” than robots –just as bourgeois Victorians felt their dignity impugned when they learned of their kinship with the apes. Or perhaps they fear that the news that we are apes or robots will result in the proletariat adopting the habits of King Kong or ArnoldSchwarzenegger. Both responses seem to me more than a little silly. I certainly noticed no lossin self-importance when I gave up the ghost in my own machine. Nor did my change of heart seem to require that I alter my behavior at all. Indeed, the fear that society will fall apart if people learn of their true nature seems to me absurd. If people are apes or robots, then they arealready behaving like apes or robots!’ Binmore, Ken, Playing Fair, Cambridge, Mass., 1994, p.231Google Scholar.

³⁴ In chapter two of Utilitarianism, Institutions, and Justice and more specifically, in ‘Moral Adaptions and Thought Experiments in Ethics’, unpublished paper, 1996Google Scholar.

³⁵ In still more exotic contexts, our ordinary intuitions are probably worse than misleading. A friend of mine who was once a teaching assistant in a course on quantum electrodynamics (QED) was fond of the following pedagogical device. ‘When encountering a problem in QED,’ he would tell them, ‘first consult your intuitions as to the answer. That answer is wrong. Now go back and do the calculations like you were supposed to.’

³⁶ Adapted from Gilovich, p. 17.