•  205
    Utilitarianism with and without expected utility
    with David McCarthy and Joaquin Teruji Thomas
    Journal of Mathematical Economics 87 77-113. 2016.
    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
  •  101
    We generalize Harsanyi's social aggregation theorem. We allow the population to be infinite, and merely assume that individual and social preferences are given by strongly independent preorders on a convex set of arbitrary dimension. Thus we assume neither completeness nor any form of continuity. Under Pareto indifference, the conclusion of Harsanyi's theorem nevertheless holds almost entirely unchanged when utility values are taken to be vectors in a product of lexicographic function spaces. T…Read more
  •  77
    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.
  •  118
    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