¹ Bradshaw's General Railway and Steam Navigation Guide, No. 921, April, 1910, reprinted Newton Abbot, 1968, pp. 549, 643.

² Schelling, Thomas C., The Strategy of Conflict, New York, 1963Google Scholar, especially chs, 3, 4; Lewis, David K., Convention, Cambridge, Mass., 1969Google Scholar, ch. 1. The term ‘salience’ (sees. V-VIII infra.) comes from Lewis, p. 35.

³ Hodgson, D.H., Consequences of Utilitarianism, Oxford, 1967Google Scholar.

⁴ See my paper, “Reason and Maximization”, Canadian Journal of Philosophy, IV, March 1975. pp. 411–33, on the relation between rationality and utility-maximization. I do not regard the maximizing conception of practical rationality as fully satisfactory, out its entrenchment in our thought makes it the appropriate starting point for this enquiry, and its inadequacies do not manifest themselves at the fairly simple level of a theory of rational coordination.

⁵ Nash, John F.. “Non-cooperative games”, Annuls of Mathematics, 54, 1951, pp. 286–95.CrossRefGoogle Scholar

⁶ A.W. Tucker's Prisoner's Dilemma is the classic example of such a situation. See my paper. “Rational Cooperation”, Nous, VIII, March 1974, pp. 53–65.

⁷ Note that the principle of coordination may not be applied to a situation n i the following iterated manner. Suppose a situation with three or more people, and a unique best equilibrium, so that the principle determines a particular action for each. Now take the action so determined for one of the persons as a fixed circumstance, eliminating that person from consideration as an agent. Consider the reduced situation involving the remaining two or more people. I n this reduced situation there may be a unique best equilibrium differing from the best equilibrium in the situation prior to reduction. If the coordination principle were applied to this reduced situation, it would determine a different action for each of the persons involved than that determined for them in the situation prior to reduction. This is clearly inadmissible, so we must not apply the principle to situations reduced by taking the actions which it requires for certain persons as fixed circumstances. The general problem which is created by reduction is discussed in my paper, “The Impossibility of Rational Egoism”, Journal of Philosophy, LXXI, August 15, 1974, pp. 439–56.

⁸ Hodgson, op. cit. Numbers in parentheses following quotations refer to pages from this book.

⁹ A very brief sketch of the type of argument I employ is found in J.L. Mackie, “The Disutility of Act-Utilitarianism”, Philosophical Quarterly, 23, October, 1973, pp. 290–1. I was, of course, unfamiliar with Mackie's argument when the principal draft of this paper was completed in July, 1973.

¹⁰ The second interpretation was first suggested to me by André Gombay, in discussing an earlier version of this paper. It was advanced more directly as the interpretation of Hodgson's argument in a communication from David Bray-brooke, whose comments were very helpful in leading me to the present section VII of the paper.

¹¹ Note that it would not be admissible to add a further principle requiring, say, that each person perform that action with the salient outcome as one of its outcomes, if there is a unique salient outcome. For such a principle might well be incompatible with the act-utilitarian principle, and even if it were restricted t o avoid such incompatibility, it would not be based on the utilities of the consequences of particular actions.

¹² The matrix values are calculated as follows. The outcome if each of us seeks the salient outcome, is the name as the outcome if I go to St Pancras and you travel from London Road. The outcome if I seek the salient outcome and you ignore it, is an equiprobable mix of the outcomes of my going to St Pancras and you travelling from London Road, and my going to St Pancras and you travelling from Leicester Central. Its utility to each is thus the sum of half of the utilities of these outcomes. The utilities of the outcome if I ignore salience and you seek it are determined similarly. The outcome if each of us ignores the salient outcome is an equiprobable mix of the four possible outcomes; its utility to each is thus the sum of one-quarter of the utilities of each of these outcomes.

¹³ Cf. Lewis, op. cit., pp. 36–51.

¹⁴ This rudimentary form is related to the “low view” of promises discussed by F.S. McNeilley, “Promises De-Moralized”, Philosophical Review, LXXXI, January, 1972, pp. 63–81.

¹⁵ Jan Narveson argues this point informally in “Promising, Expecting, and Utility”, Canadian Journal of Philosophy, I, 1971, pp. 220–8.

¹⁶ Or it may be that our conception of rationality is inadequate. A utility-maximizing conception of rationality may be incompatible with our ordinary conception of obligations and duties; if so, one must be abandoned. But which one?

¹⁷ Cf. “Reason and Maximization”, sees. VI, VIII.

¹⁸ I discuss the problem of securing an optimal outcome in the absence of optimal equilibria in “Rational Cooperation”.