In the wake of J. S. Mill's withering attacks on Bentham's over-simplified moral arithmetic, most philosophers have shied away from a mathematical model of utilitarianism. C. L. Sheng has long criticized this retreat, calling instead for a return to the earlier utilitarian hopes of founding a science of ethics complete with mathematical rigour. In A Defense of Utilitarianism, Sheng returns to his unified utilitarian theory (UUT), first articulated in his A New Approach to Utilitarianism (1991), with the dual aims of interpreting the principle of utility more precisely and then proposing UUT as a solution to the supposed conflict between utility and justice.

After a basic introductory chapter, the next three chapters of Sheng's book sketch an overview of his understanding of the nature of the principle of utility and his conception of value. Although ostensibly one of the main purposes of the book is to defend a rigorous and explicit account of the principle of utility, Sheng does disappointingly little in that regard. His most interesting (and controversial) points in these chapters are often presented without an accompanying argument, with the reader instead referred to Sheng's earlier writings.

Chapters 5–8 are the real heart of Sheng's defence of UUT. Applying decision theory to utilitarianism, Sheng offers an updated model of Bentham's moral arithmetic. In place of Bentham's propinquity, fecundity and the like, Sheng proposes a number of variables to include in his calculations, among them the value of the direct consequences for society, the value of the feeling of moral satisfaction an agent gets from having performed the right action (expressed as a constant called the coefficient of morality), the value of societal praise or blame for an action, and a value to express any secondary selfish motivations that benefit only the agent performing the action.

In chapters 9–11, Sheng turns his attention to resolving a number of objections to utilitarianism, objections that he claims UUT resolves. Chapter 9 attempts to reconcile justice and utility and to address the act/omission distinction raised by trolley problems. In chapter 10, Sheng argues that UUT can resolve the is/ought gap that is particularly acute for teleological theories of ethics. And finally in chapter 11, Sheng defends UUT as a viable moral theory, contrasting its strengths with the weaknesses of both act- and rule-utilitarianism.

Sheng performs yeoman's duty in exhaustively cataloguing the various values at stake in a utilitarian decision. His application of those values is somewhat more problematic, as many of his applications require assumptions that appear to be unwarranted. For example, Sheng reconciles a number of objections to utilitarianism (notably the tension between justice and utility and the conflict between the right and the good) by adding a variable representing ‘societal value’ to his utility calculations. Societal value, defined as the value added (or subtracted) by an action that exemplifies (or violates) a moral principle, functions as a magic bullet for reconciling justice with utility: if action A maximizes utility while being unjust, then we can simply add a large negative societal value to A until justice and utility coincide perfectly. The right and the good can then be reconciled in an analogous manner. Besides being somewhat ad hoc, Sheng's introduction of societal value is not clearly an improvement over, or even a real change from, standard act-utilitarian accounts. Like most act-utilitarians, Sheng ultimately relies upon the empirical claim that breaking general rules creates enough disutility to make breaking the rule unwarranted. Reliance upon that empirical claim still leaves UUT open to the counter-objection that, in principle, an unjust action could have a large enough utility and a small enough societal value that UUT ought to endorse it. Sheng has isolated and quantified a (dubious?) empirical claim, but he fails to provide any reasons at all for thinking that the claim is true.

My deeper worry regarding UUT is that it may not be appropriate to call the theory utilitarian at all. Indeed, Sheng makes the rather shocking claim that, in calculating utilities, only the utility of the recipient of the action and the utility of the agent need to be considered. The utility of everyone else potentially affected by the action is part of the general environmental condition of the world. Drawing heavily on a distinction between positive and negative duties, Sheng argues that to the extent that the agent is not directly responsible for having created the initial environmental conditions, he has no duty to correct them. The obvious targets of this claim are what Sheng calls ‘hard-line utilitarians’, or those who hold that a utilitarian is obligated to consider the needs of the poor in making any decision. Sheng objects that the notion that I would have to consider the utilities of the poor whenever I contemplate spending money but would not need to do so when I consider other types of actions is itself a reductio of hard-line utilitarianism.

It is hard to feel much relief at Sheng's ‘rescue’ of utilitarianism, for his rearticulation arguably creates more problems than it solves. In allowing me to make decisions that are unconstrained by external facts about the world, Sheng opens up the possibility that it might, for example, be perfectly permissible for me to sell a machine gun to a known serial killer. Sheng's argument betrays, I think, a fundamental incompatibility between utilitarianism and decision theory. Sheng sees all decisions as fundamentally a choice between two options; in all of his examples, the available choices always boil down to A or not-A. Some of those discrete sets of choices involve spending money and others do not; on that view, it is not unreasonable to complain that I would have to consider the utilities of others in choosing between some sets of actions and would not have to do so when considering other sets of choices. So, for example, I would have to consider the utilities of others when deciding whether or not to spend $10 to watch a movie with a friend, but I would not have to make such a calculation when deciding whether or not to spend the evening discussing a book with a friend. But it is not at all clear that a utilitarian ought to view choice sets so discretely. As a utilitarian, my duty is to maximize utility, not simply to choose the better of A or not-A; I would seem to have a commitment to choose the action, from all of those available to me, that will create the most utility. Since one possible action for me will always involve spending money, there will not be any real distinction between choices that involve spending money and choices that do not.

In the final analysis, I am not convinced that Sheng has constructed a utilitarian theory at all. Despite his claim that UUT is a compromise between act- and rule-utilitarianism, I think that, given Sheng's strong reliance upon the distinction between positive and negative duties and his insistence on holding agents accountable only for the consequences that their own actions have brought about, it might be more accurate to read UUT as a compromise between utilitarianism and some form of deontology. Still, Sheng offers a provocative extension of his work on UUT; those who have followed that work will benefit from reading A Defense of Utilitarianism. Those just encountering Sheng might find their time better spent reading A New Approach to Utilitarianism.