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1 See Kydland, Finn and Prescott, Edward, “Rules Rather Than Discretion: The Inconsistency of Optimal Plans,” Journal of Political Economy 85, no. 3 (1977): 473–92, among many others. Glazer, Amihai and Rothenberg, Lawrence S. outline policy issues involving time consistency issues in Why Government Succeeds and Why It Fails (Cambridge, CA: Harvard University Press, 2005).

2 Parfit, Derek, Reasons and Persons, rev. ed. (Oxford: Clarendon Press, 1987).

3 Ibid., 67, provides a string of related examples and conundrums.

4 Some of these dilemmas resemble the Sorites problem, which typically involves nonlinear effects. A classic example of the Sorites problem is to ask how many stones constitute a pile. The contribution of any single stone to the “pileness” of the pile is zero or very small, yet the accretion of successive stones brings a pile into being. The analogy is not perfect, because our definition of “pile” is fuzzy, a complication which does not arise in the firing squad case (the death of the victim is unambiguous). Temkin, Larry S. considers how the Sorites problem differs from intransitivity and vagueness as issues in moral philosophy in “A Continuum Argument for Intransitivity,” Philosophy and Public Affairs 25, no. 3 (1996): 175210.

5 An extensive literature covers the practical arguments in favor of rules. See Hayek, Friedrich A., The Constitution of Liberty (Chicago: University of Chicago Press, 1960); Brennan, Geoffrey and Buchanan, James M., The Reason of Rules (Indianapolis, IN: Liberty Fund, 2000); and Epstein, Richard, Simple Rules for a Complex World (Cambridge, MA: Harvard University Press, 1997).

6 The literature here is enormous. See, for instance, Brandt, Richard, “Toward a Credible Theory of Utilitarianism,” in Castaneda, Hector-Neri and Nakhnikian, George, eds., Morality and the Language of Conduct (Detroit, MI: Wayne State University Press, 1963): 107–43; Lyons, David, Forms and Limits of Utilitarianism (Oxford: Clarendon Press, 1965); Regan, Donald H., Utilitarianism and Cooperation (Oxford: Oxford University Press, 1980); Slote, Michael, From Morality to Virtue (Oxford: Oxford University Press, 1992); Hooker, Brad, Ideal Code, Real World: A Rule-Consequentialist Theory of Morality (Oxford: Clarendon Press, 2000): 93111; Mackie, John Leslie, Persons and Values: Selected Papers, Vol. II (Oxford: Clarendon Press, 1985); Scarre, Geoffrey, Utilitarianism (New York: Routledge, 1996); and Feldman, Fred, Utilitarianism, Hedonism, and Desert (Cambridge: Cambridge University Press, 1997), among many others. This problem has been present in rule utilitarianism since William Paley in the eighteenth century; see Schneewind, J. B., Sidgwick's Ethics and Victorian Moral Philosophy (Oxford: Clarendon Press, 1977), 125–27.

7 Friedman, Milton, “The Real Free Lunch: Markets and Private Property,” in Boaz, David, ed., Toward Liberty: The Idea That Is Changing the World (Washington DC: Cato Institute, 2002), 5562.

8 Demsetz, Harold, “Information and Efficiency: Another Viewpoint,” Journal of Law and Economics 12, no. 1 (1969): 122.

9 This ranked example is drawn from Cowen, Tyler, “The Epistemic Problem Does Not Refute Consequentialism,” Utilitas 18, no. 4 (2006): 383–99. On the concept of utopianism in the economics literature, see Philbrook, Clarence, “'Realism' in Policy Espousal,” American Economic Review 43, no. 5 (1953): 846–59, reprinted in Klein, Daniel B., ed., What Do Economists Contribute? (Washington, DC: Cato Institute, 1999), 6986; Dahlman, Carl J., “The Problem of Externality,” Journal of Law and Economics 22, no. 1 (1979): 141–62; Brown, Pamela J., Deadweight Loss: A Nonexistence Theorem (unpublished manuscript, California State University, Northridge, 1988); and Klein, Daniel B., ed., What Do Economists Contribute? (Washington, DC: Cato Institute, 1999).

10 Parfit, Reasons and Persons, Part I, chap. 3.

11 Norcross, Alastair argues that we need to consider the best available action relative to alternatives, and discusses the ambiguities in defining exactly what those alternatives are, in “Good and Bad Actions,” The Philosophical Review 106, no. 1 (1997): 133. On the relevance of related ideas for the free will controversies, see Dennett, Daniel C., Elbow Room: The Varieties of Free Will Worth Wanting (Cambridge, MA: MIT Press, 1984). For discussion of the meanings of “if” and “can” in ordinary language philosophy, see Austin, J. L., Philosophical Papers (Oxford: Clarendon Press, 1961); and Pears, D. F., “Ifs and Cans,” in Essays on J. L. Austin (Oxford: Clarendon Press, 1973). Blackburn, Simon considers general issues involving morals and modal logic in “Morals and Modals,” in Blackburn, , Essays in Quasi-Realism (Oxford: Oxford University Press, 1993), 5274.

12 In fairness to Fourier, he was also an early prophet of the steam locomotive, a view for which he was ridiculed in his time; see Beecher, Jonathan, Charles Fourier: The Visionary and His World (Berkeley: University of California Press, 1986), 59. On the lemonade idea, see ibid., 125.

13 The literature on utopias raises related questions, although not usually in a philosophic or rational choice framework. Kolnai, Aurel writes: “How exactly can we distinguish between the proper pursuit of the good and its perfectionist aberration?” in Kolnai, The Utopian Mind and Other Papers: A Critical Study in Moral and Political Philosophy, ed. Dunlop, Francis (London: Athlone, 1995), 17. Manuel, Frank E. and Manuel, Fritzie P. note that “one man's trivial revision is another man's upheaval” in Utopian Thought in the Western World (Cambridge, MA: Belknap Press of Harvard University Press, 1979), 8. Mannheim, Karl refers to the “difficulty in defining precisely what, at a given period, is to be regarded as ideology, and what as utopia” in Ideology and Utopia: An Introduction to the Sociology of Knowledge (New York: Harcourt, 1936), 203. Since at least Friedrich Engels, this topic has been a staple of socialist debate as well. See Engels, Friedrich, Socialism: Utopian and Scientific (Peking: Foreign Languages Press, 1975). For a survey of some definitions of utopia, see Levitas, Ruth, The Concept of Utopia (Syracuse, NY: Syracuse University Press, 1990), 3. See also Davis, J. C., “The History of Utopia: The Chronology of Nowhere,” in Alexander, Peter and Gill, Roger, eds., Utopias (London: Duckworth, 1984): 118; and Sargent, Lyman Tower, “Utopian Themes: Themes and Variations,” in Schaer, Roland, Claeys, Gregory, and Sargent, Lyman Tower, eds., Utopia: The Search for the Ideal Society in the Western World (New York: The New Public Library/Oxford University Press, 2000), 815. Goodwin, Barbara and Taylor, Keith consider the role that concepts of utopia have played in political debate in The Politics of Utopia: A Study in Theory and Practice (New York: St. Martin's Press, 1982).

14 On various modal debates, see Loux, Michael J., The Possible and the Actual: Readings in the Metaphysics of Modality (Ithaca, NY: Cornell University Press, 1979); Forbes, Graeme, The Metaphysics of Modality (Oxford: Clarendon Press, 1985); Lewis, David, On the Plurality of Worlds (New York: Basil Blackwell, 1986); Armstrong, D. M., A Combinatorial Theory of Possibility (Cambridge: Cambridge University Press, 1989); Lycan, William G., Modality and Meaning (Dordrecht: Kluwer Publishers, 1994); Hitchcock, Christopher, “Farewell to Binary Causation,” Canadian Journal of Philosophy 26, no. 2 (1996): 267–82; Pruss, Alexander Robert, “Possible Worlds: What They Are Good For and What They Are Not” (unpublished doctoral dissertation, University of Pittsburgh, 2001); Sider, Theodore, “The Ersatz Pluriverse,” The Journal of Philosophy 99, no. 6 (2002): 279315; Gendler, Tamar Szabo and Hawthorne, John, eds., Conceivability and Possibility (Oxford: Clarendon Press, 2002); and Divers, John, Possible Worlds (London: Routledge, 2002).

15 Parmenides argued that the world could not be any different. The literature on theodicy considers whether God made the “best possible world” and what it means to say that other worlds are possible. See Adams, Robert M., The Virtue of Faith and Other Essays in Philosophical Ideology (New York: Oxford University Press, 1987); Adams, Robert M., Leibniz: Determinist, Theist, Idealist (New York: Oxford University Press, 1994); and Plantinga, Alvin, The Nature of Necessity (Oxford: Clarendon Press, 1989).

16 For a more general survey of utopian thinking, see Manuel and Manuel, Utopian Thought in the Western World.

17 In formal terms, the Shapley solution looks at all possible differing “coalitions” (combinations of actions or abstentions from action, in the firing squad example) and measures the differing marginal values of an individual unit to the coalition. These marginal values are then averaged across all of the possible combinations of units. In the firing squad example, for instance, the Shapley value averages a single shooter's marginal impact across “all six of us shoot,” “only the first five of the six shoot,” “only the last five of the six shoot,” “only these three of the six shoot,” “only I shoot,” and so on, across all the possible combinations. We will then find that the Shapley value for a single marksman is positive, but less than the value of an individual life. On the bargaining theory foundations for the Shapley value, see Roth, Alvin E., “Axiomatic Models of Bargaining,” Lecture Notes in Economics and Mathematical Systems, No. 170 (New York: Springer Verlag, 1979); and Gul, Faruk, “Bargaining Foundations of Shapley Value,” Econometrica 57, no. 1 (1989): 8195.

18 David Lewis has suggested some standards for ranking worlds in terms of their similarity, and along these lines we might regard the more similar worlds to our own as “more possible” or “less utopian.” See Lewis, David, “Counterfactual Dependence and Time's Arrow,” Noûs 13, no. 4 (1979): 472. For a treatment of degrees of possibility, see Forbes, The Metaphysics of Modality, chap. 7.

19 Note that we should not identify feasibility with the notions of probability or likelihood. Feasibility refers in some manner to the “closeness” of some other world to our own, whether or not we expect that world to occur. Blinking your eyes one more time in a day, each day, might be quite feasible in the common-sense use of that term, although we do not necessarily expect such an act to occur with a high probability. Conditional on the number of blinks changing, the chance that the change is exactly one blink might be quite small. This example suggests that feasibility and probability are distinct concepts and that a high degree of feasibility does not have to mean a high degree of probability.

20 On costs of adoption and internalization and rule utilitarianism, see Richard Brandt, “Toward a Credible Theory of Utilitarianism,” in Castaneda and Nakhnikian, eds., Morality and the Language of Conduct, 107–43; and Hooker, Ideal Code, Real World, 78–79. On varieties of rule utilitarianism more generally, see Scarre, Utilitarianism, 122–32.

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