Abstract
Would rational act-utilitarians keep their agreements? Suppose two highly rational act-utilitarians agree to meet for a walk in the park. The best outcome they can achieve is to meet as agreed, and the next best is for both to stay home and read. Because each would find it distressing to come and not find the other, the worst outcome they can achieve is for one to come to the park and the other to stay at home. Suppose everything above is common knowledge between them, in the sense that each knows it, each knows the other knows it, each knows the other knows that he knows it, and so on ad infinitem. Under these circumstances, either person would keep the agreement if he knew the other would, for he could then conclude that his coming as agreed would yield the best outcome, that they meet, whereas his staying at home would yield the worst outcome, that one comes and the other stays home. On the other hand, either would break the agreement if he knew that the other would break it, for in that case he could reason that if he came as agreed, he would achieve the worst outcome, that one comes and the other stays at home, whereas if he stayed home, he would achieve the intermediate outcome that both stay home. All this will be common knowledge between the two. Does any of it, though, give either of them grounds for keeping the agreement?
Work on this paper was supported by a grant from the National Endowment for the Humanities.
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Notes
As I am using the term,’ subjectively right’, then, an agent may be mistaken in thinking an act subjectively right. He may hold an incorrect moral theory; he may have irrational non-moral beliefs and probability ascriptions; or he may misapply a correct moral theory to rational non-moral beliefs and probability ascriptions. For discussions of this subjective sense, see Brandt (1959, pp. 360-67).
In Gibbard and Harper (1978), we argue that this probability should be the probability of a subjunctive conditional ‘If I were to do act A, outcome would obtain.’ Another view, which we argue against, is that the relevant probability is the conditional probability of outcome on my doing A. We owe the distinction to David Lewis, and our interpretation of it to Robert Stalnaker. For the purposes of this paper, it does not matter which of these two views the reader takes.
This argument is given in Sobel (1976). See especially footnotes 6 and 7.
Cf. Ross (1930, p. 39) and Brandt (1959, pp. 387-8).
These conditions are equivalent, in the present Framework, to the axioms given by von Neumann and Morgenstern (1947, p. 26).
The lexical maximin ordering of Rawls (1971, p. 83), applied to prospects, violates the Archimedean condition but satisfies the Compounding Condition. The rule would be this: Of two prospects, prefer the one with the better worst outcome. In case of ties by this criterion, prefer the one whose worst outcome has the lower probability. In case of ties by this criterion, remove the worst outcomes and start over.
In Gibbard and Harper (1978), we argue that these states should be causally independent of the acts in question. An alternative view, which we argue against, is that the states should be stochastically independent of the acts.
In Section 9, the example of a surprise birthday party showed a violation of (3a*), and the example of a promise to a dying woman to take care of her child showed a violation of (3b*).
References
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Gibbard, A. (1978). Act-Utilitarian Agreements. In: Goldman, A.I., Kim, J. (eds) Values and Morals. Philosophical Studies Series in Philosophy, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7634-5_6
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