John Harsanyi has provided an intriguing argument that social welfare can be expressed as a weighted sum of individual utilities. His theorem has been criticized on the grounds that a central axiom, that social preference satisfies the independence axiom, has the morally unacceptable implication that the process of choice and considerations of ex ante fairness are of no importance. This paper presents a variation of Harsanyi's theorem in which the axioms are compatible with a concern for ex ante fairness. The implied mathematical form for social welfare is a strictly quasi-concave and quadratic function of individual utilities.

Preference relations over two-stage lotteries are analyzed. Empirical evidence indicates that decisionmakers do not always behave in accordance with the reduction of compound lotteries axiom, but they seem to satisfy a compound independence axiom. Although the reduction and the compound independence axioms, together with continuity, imply expected utility theory, each of them by itself is compatible with all possible preference relations over simple lotteries. Using these axioms, the author analyzes three different versions of expected utility for two-stage lotteries. The author suggests several different compound dominance axioms as possible replacements of the reduction axiom, which are strictly weaker than the reduction of compound lotteries axiom.

One of the most puzzling paradoxes in decision theory is the preference reversal phenomenon. This phenomenon seems to contradict the transitivity axiom, for a long time, one of the cornerstones of utility theory. This paradox is established whenever a decision maker prefers lottery X to lottery Y, but is willing to put a lower selling price on X than on Y. Such experiments, first reported by Harold Lindman, 1971; and Sarah Lichtenstein and Paul Slovic, 1971, were repeated by David Grether and Charles Plott, 1979; Werner Pommerehne et al., 1982; and Robert Reilly, 1982. Although the later researchers improved the mechanism through which the selling price emerges, they all found systematic reversals. A new approach to this problem was developed by Charles Holt, 1986, and Edi Karni and Zvi Safra, 1987. From two different starting points, these authors showed that the preference reversal phenomenon does not necessarily prove a violation of the transitivity axiom, as it may contradict the independence axiom. This implies that people do not maximize expected utility, but in that case the preference reversal phenomenon becomes just another evidence against expected utility theory, but not against the transitivity axiom. These results have their own disadvantages. Although the independence axiom is not as fundamental as transitivity, it is nevertheless very appealing on normative grounds. Of course, the preference reversal phenomenon necessarily contradicts at least one of the assumptions of expected utility theory, but empirical evidence shows that despite its normative appeal, violations of the reduction of compound lotteries axiom may happen (see, for example, Joshua Ronen, 1971, and Doug Snowball and Clif Brown, 1979). In this paper I therefore suggest a decision mechanism for the preference reversals lotteries which is transitive and satisfies the independence axiom, but not the reduction axiom.

This paper shows that a minimal degree of consideration for other people's well‐being enables society to agree that one social policy is the best. I offer axioms that imply that this best policy maximizes a weighted sum of individual utilities. The weight of each individual is the inverse of his or her maximal possible utility from social endowments. The suggested policy is not sensitive to the choice of the von Neumann‐Morgenstern utilities. The key axiom is that individuals agree that giving all the endowments always to one person is as bad as giving them to any other person.

Consider an economy with equal amounts of N types of goods, to be allocated to agents with strict quasi-convex preferences over lotteries. We show that ex ante, all Pareto-efficient allocations give almost all agents lotteries over at most two outcomes. Our results provide a simple criterion showing that many popular allocation mechanisms are ex ante inefficient. For the case of identical preferences, we establish existence of an efficient solution where all lotteries used are equally attractive. Assuming the reduction axiom, social welfare deteriorates by first randomizing over these binary lotteries. Efficient ex ante equality is achieved if agents satisfy the compound-independence axiom.

Rabin (2000) proved that a low level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. Rabin's arguments strongly depend on expected utility theory, but we show that similar arguments apply to general non-expected utility theories.

There are several solutions to the Nash bargaining problem in the literature. Since various authors have expressed preferences for one solution over another, we find it useful to study preferences over solutions in their own right. We identify a set of appealing axioms on such preferences that lead to unanimity in the choice of solution, which turns out to be the solution of Nash.

John Harsanyi has provided an intriguing argument that social welfare can be expressed as a weighted sum of individual utilities. His theorem has been criticized on the grounds that a central axiom, that social preference satisfies the independence axiom, has the morally unacceptable implication that the process of choice and considerations of ex ante fairness are of no importance. This paper presents a variation of Harsanyi's theorem in which the axioms are compatible with a concern for ex ante fairness. The implied mathematical form for social welfare is a strictly quasi-concave and quadratic function of individual utilities.