¹ Smith, Holly M., ‘Measuring the Consequences of Rules’, Utilitas 22 (2010), pp. 413–33CrossRefGoogle Scholar.

² Smith, ‘Measuring the Consequences’, p. 421; Hooker, Brad, Ideal Code, Real World (Oxford, 2000), pp. 124–5Google Scholar; Lyons, David, Forms and Limits of Utilitarianism (Oxford, 1965), pp. 128–31CrossRefGoogle Scholar.

³ Smith, ‘Measuring the Consequences’, p. 421.

⁴ Ridge, Michael, ‘Introducing Variable-Rate Rule-Utilitarianism’, The Philosophical Quarterly 56 (2006), pp. 249–50CrossRefGoogle Scholar.

⁵ Smith, ‘Measuring the Consequences’, pp. 421, 423.

⁶ Smith, ‘Measuring the Consequences’, p. 421.

⁷ Brad Hooker, ‘Rule Consequentialism’, Stanford Encyclopedia of Philosophy, <http://plato.stanford.edu/archives/spr2011/entries/consequentialism-rule/> (2011); Rachael Briggs, ‘Normative Theories of Rational Choice: Expected Utility’, Stanford Encyclopedia of Philosophy, <http://plato.stanford.edu/entries/rationality-normative-utility/> (2014).

⁸ Many utilitarians have suggested using expected utility in one way or another. For a recent rule-utilitarian who uses expected utility, see Hooker, Ideal Code, Real World, pp. 1–2.

⁹ For the sake of simplicity, I will assume – as Smith does – that universal acceptance leads to universal compliance. Nothing in my arguments will turn on this, however.

¹⁰ Smith, ‘Measuring the Consequences’, p. 423.

¹¹ Smith, ‘Measuring the Consequences’, pp. 423–4.

¹² Smith, ‘Measuring the Consequences’, p. 424.

¹³ Smith, ‘Measuring the Consequences’, n. 30.

¹⁴ I believe this indeterminacy is actually an instance of what game theorists call multiple equilibria, and the river pollution case is an instance of what is known as an assurance game in game theory. In order to map the assurance game onto the river pollution case, one simply needs to reinterpret the game theoretic payoffs as ‘moral payoffs’ that measure the moral value of each outcome, as judged by the accepted moral code. This analogy is good for the rule-utilitarian, because assurance games have been observed to be resolved quickly with communication. An introduction to the assurance game can be found in Dixit, Avinash K. and Skeath, Susan, Games of Strategy, 2nd edn. (New York, 2004), pp. 105–8Google Scholar, 394–6.

¹⁵ This iteration of expected value calculations is exactly how expected utility theory deals with cases of nested uncertainty (the paradigm case being a lottery whose outcomes are further lotteries rather than payoffs). Iterated expected values are also used in Tobia, Kevin, ‘Rule Consequentialism and the Problem of Partial Acceptance’, Ethical Theory and Moral Practice 16.3 (2012), pp. 643–52CrossRefGoogle Scholar. However Tobia uses them to solve a different problem of how to evaluate a moral code whose expected consequences change depending on the level of social acceptance.

¹⁶ More generally, all the graphs she uses to illustrate rule-utilitarianism have expected social utility on the y-axis.

¹⁷ Cadsby, Charles Bram and Maynes, Elizabeth, ‘Voluntary Provision of Threshold Public Goods with Continuous Contributions: Experimental Evidence’, Journal of Public Economics 71.1 (1999), pp. 53–73 CrossRefGoogle Scholar.

¹⁸ The key difference is that participants in these experiments are not told to follow any particular moral code.

¹⁹ Thanks to the Editor-in-Chief for urging me to address this.

²⁰ Rawls, John, A Theory of Justice, rev. edn. (Oxford, 1999), pp. 132–4Google Scholar. Thanks to the Editor-in-Chief for suggesting this.

²¹ Smith, ‘Measuring the Consequences’, pp. 426–8. Despite the way I have presented it, this problem actually arises at 100 per cent compliance too. To see this, imagine a population that is fully compliant with some moral code. They still have to make some decisions between options that are all permissible according to this code – such as the decision between taking the bus or train to work, for instance. Choosing one option or another will have different effects on the overall consequences. But it is indeterminate as to how they would choose, and so Smith's second problem similarly applies.

²² Even with universal acceptance of and compliance with the law, three different patterns of action might emerge – only parent A takes leave, or only parent B takes leave, or both A and B take leave. And it is epistemically indeterminate as to which one will actually obtain.

²³ Suppose 60 per cent of people do not flout the ban – this means that 40 per cent do flout it. Some proportion of this 40 per cent will choose to pay $500, and the rest will go to jail – but it is epistemically indeterminate as to what the proportions might be.

²⁴ Many thanks to Weng Hong Tang and Christopher Anthony Brown for the comments and discussion. I am also grateful to the Editor-in-Chief of this journal for his helpful suggestions. Any errors in this article are my own.