•  31
    A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-re…Read more
  •  741
    Utilitarianism with and without expected utility
    Journal of Mathematical Economics 87 77-113. 2020.
    We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference…Read more
  •  356
    We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent…Read more
  •  321
    Continuity and completeness of strongly independent preorders
    Mathematical Social Sciences 93 141-145. 2018.
    A strongly independent preorder on a possibly infinite dimensional convex set that satisfies two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfies two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') m…Read more
  •  294
    We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infinite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfies a condition that we call Polarization.
  •  927
    Probability in ethics
    In Alan Hájek & Christopher Hitchcock (eds.), The Oxford Handbook of Philosophy and Probability, Oxford University Press. 2016.
    The article is a plea for ethicists to regard probability as one of their most important concerns. It outlines a series of topics of central importance in ethical theory in which probability is implicated, often in a surprisingly deep way, and lists a number of open problems. Topics covered include: interpretations of probability in ethical contexts; the evaluative and normative significance of risk or uncertainty; uses and abuses of expected utility theory; veils of ignorance; Harsanyi’s aggreg…Read more
  •  176
    Self torture and group beneficence
    Erkenntnis 47 (1): 129-144. 1997.
    Moral puzzles about actions which bring about very small or what are said to be imperceptible harms or benefits for each of a large number of people are well known. Less well known is an argument by Warren Quinn that standard theories of rationality can lead an agent to end up torturing himself or herself in a completely foreseeable way, and that this shows that standard theories of rationality need to be revised. We show where Quinn's argument goes wrong, and apply this to the moral puzzles
  •  211
    Utilitarianism and prioritarianism II
    Economics and Philosophy 24 (1): 1-33. 2008.
    A natural formalization of the priority view is presented which results from adding expected utility theory to the main ideas of the priority view. The result is ex post prioritarianism. But ex post prioritarianism entails that in a world containing just one person, it is sometimes better for that person to do what is strictly worse for herself. This claim may appear to be implausible. But the deepest objection to ex post prioritarianism has to do with meaning: ex post prioritarianism is not a …Read more
  •  133
    Harming and allowing harm
    Ethics 110 (4): 749-779. 2000.
    The article takes as its starting point the assumption that (a) competing accounts of moral rules should be judged by the distribution of benefits and burdens which would arise from everyone accepting these rules, and that (b) these benefits and burdens are understood in a way which has a substantial resource or freedom-based component. This starting point is compatible with contractualism and various forms of rule consequentialism, and will yield a morality in which people have significant fre…Read more
  •  169
    Distributive equality
    Mind 124 (496): 1045-1109. 2015.
    Egalitarians think that equality in the distribution of goods somehow matters. But what exactly is egalitarianism? This article argues for a characterization based on novel principles essentially involving risk. The characterization is then used to resolve disputed questions about egalitarianism. These include: the way egalitarianism is concerned with patterns, in particular its relationship to strong separability; the relationship between egalitarianism and other distributive views, such as con…Read more
  •  101
    Risk-free approaches to the priority View
    Erkenntnis 78 (2): 421-449. 2013.
    Parfit advertised the priority view as a new and fundamental theory in the ethics of distribution. He never discusses risk, and many writers follow suit when discussing the priority view. This article formalizes two popular arguments for a commonly accepted risk-free definition of the priority view. One is based on a direct attempt to define the priority view, the other is based on a contrast with utilitarianism and egalitarianism. But neither argument succeeds, and more generally, it is not pos…Read more
  •  172
    The two envelope paradox can be dissolved by looking closely at the connection between conditional and unconditional expectation and by being careful when summing an infinite series of positive and negative terms. The two envelope paradox is not another St. Petersburg paradox and that one does not need to ban talk of infinite expectation values in order to dissolve it. The article ends by posing a new puzzle to do with infinite expectations.
  •  102
    Theoretical defenses of the principle of double effect (pde) due to Quinn, Nagel and Foot are claimed to face severe difficulties. But this leaves those of us who see something in the case-based support for the pde without a way of accounting for our judgments. This article proposes a novel principle it calls the mismatch principle, and argues that the mismatch principle does better than the pde at accounting for our judgments about cases and is also theoretically defensible. However, where the …Read more
  •  565
    The priority view
    Economics and Philosophy 33 (2). 2017.
    According to the priority view, or prioritarianism, it matters more to benefit people the worse off they are. But how exactly should the priority view be defined? This article argues for a highly general characterization which essentially involves risk, but makes no use of evaluative measurements or the expected utility axioms. A representation theorem is provided, and when further assumptions are added, common accounts of the priority view are recovered. A defense of the key idea behind the priori…Read more
  •  122
    Rights, explanation, and risks
    Ethics 107 (2): 205-225. 1997.
    Theories of rights seem well equipped to explain widely accepted claims about the morality of harming. But can they explain popular claims about the morality of imposing risks of harm? Many think not. But a plausible theory of rights can explain those claims if it says we have the right that others not impose risks of harm upon us. That is a good reason to believe we have that right. There are many objections to the claim that we have that right, but none of them are sound. Among the topics cove…Read more
  •  57
    Measuring life's goodness
    Philosophical Books 48 (4): 303-319. 2007.
    Philosophers often assume that we can somehow quantitatively measure how good things are for people. But what does such talk mean? And what are the measures? In *Weighing Goods* John Broome offers one treatment of these questions. In his later *Weighing Lives* he offers a different treatment. This article discusses both positions but advocates a third. But while the three positions disagree about matters of meaning, they agree about the form of the measures. Roughly speaking, they are such that …Read more
  •  85
    Liability and risk
    Philosophy and Public Affairs 25 (3): 238-262. 1996.
    Standard theories of liability say that X is liable to Y only if Y was harmed, only if X caused Y harm, and (usually) only if X was at fault. This article offers a series of criticisms of each of these claims, and use them to construct an alternative theory of liability in which the nature of X's having imposed a risk of harm on Y is central to the question of when X is liable to Y, and for how much. The article ends with some conjectures on ignorance as an excusing condition.
  •  168
    Utilitarianism and prioritarianism I
    Economics and Philosophy 22 (3): 335-363. 2006.
    Utilitarianism and prioritarianism make a strong assumption about the uniqueness of measures of how good things are for people, or for short, individual goodness measures. But it is far from obvious that the presupposition is correct. The usual response to this problem assumes that individual goodness measures are determined independently of our discourse about distributive theories. This article suggests reversing this response. What determines the set of individual goodness measures just is th…Read more
  •  83
    Actions, beliefs, and consequences
    Philosophical Studies 90 (1): 57-77. 1998.
    On the agent-relativity thesis, what an agent ought to do is a function of the evidence available to her about the consequences of her potential actions. On the objectivity thesis, what an agent ought to do is a function of what the consequences of her potential actions would be, regardless of the evidence available to her. This article argues for the agent-relativity thesis. The main opposing argument, due to Thomson, points to cases where a bystander can see that an agent is about to do someth…Read more