Behaviour norms are considered for decision trees which allow both objective probabilities and uncertain states of the world with unknown probabilities. Terminal nodes have consequences in a given domain. Behaviour is required to be consistent in subtrees. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree. It implies that behaviour reveals a revealed preference ordering satisfying both the independence axiom and a novel form of sure-thing principle. Continuous consequentialist behaviour must be expected (...) utility maximizing. Other plausible assumptions then imply additive utilities, subjective probabilities, and Bayes' rule. (shrink)

The essays in this volume, first published in 1986, examine the philosophical foundations of social choice theory. This field, a modern and sophisticated outgrowth of welfare economics, is best known for a series of impossibility theorems, of which the first and most crucial was proved by Kenneth Arrow in 1950. That has often been taken to show the impossibility of democracy as a procedure for making collective decisions. However, this interpretation is challenged by several of the contributors here. Other central (...) issues discussed in the volume include the possibility of making interpersonal comparisons of utility, the question of whether all preferences are equally to be valued, and the normative individualism underlying the theoretical tradition. Criticisms of social choice theory are advanced and suggestions for alternative approaches are developed. (shrink)

Ramsey famously pronounced that discounting “future enjoyments” would be ethically indefensible. Suppes enunciated an equity criterion implying that all individuals’ welfare should be treated equally. By contrast, Arrow accepted, perhaps rather reluctantly, the logical force of Koopmans’ argument that no satisfactory preference ordering on a sufficiently unrestricted domain of infinite utility streams satisfies equal treatment. In this paper, we first derive an equitable utilitarian objective based on a version of the Vickrey–Harsanyi original position, extended to allow a variable and uncertain (...) population with no finite bound. Following the work of Chichilnisky and others on sustainability, slightly weakening the conditions of Koopmans and co-authors allows intergenerational equity to be satisfied. In fact, assuming that the expected total number of individuals who ever live is finite, and that each individual’s utility is bounded both above and below, there is a coherent equitable objective based on expected total utility. Moreover, it implies the “extinction discounting rule” advocated by, inter alia, the Stern Review on climate change. (shrink)

Ramsey famously condemned discounting “future enjoyments” as “ethically indefensible”. Suppes enunciated an equity criterion which, when social choice is utilitarian, implies giving equal weight to all individuals’ utilities. By contrast, Arrow accepted, perhaps reluctantly, what he called Koopmans’ :287–309, 1960) “strong argument” implying that no equitable preference ordering exists for a sufficiently unrestricted domain of infinite utility streams. Here we derive an equitable utilitarian objective for a finite population based on a version of the Vickrey–Harsanyi original position, where there is (...) an equal probability of becoming each person. For a potentially infinite population facing an exogenous stochastic process of extinction, an equitable extinction biased original position requires equal conditional probabilities, given that the individual’s generation survives the extinction process. Such a position is well-defined if and only if survival probabilities decline fast enough for the expected total number of individuals who can ever live to be finite. Then, provided that each individual’s utility is bounded both above and below, maximizing expected “extinction discounted” total utility—as advocated, inter alia, by the Stern Review on climate change—provides a coherent and dynamically consistent equitable objective, even when the population size of each generation can be chosen. (shrink)