Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation, since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We explicitly investigate the (...) short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging. (shrink)

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...) Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (shrink)

The Pareto principle states that if the members of society express the same preference judgment between two options, this judgment is compelling for society. A building block of normative economics and social choice theory, and often borrowed by contemporary political philosophy, the principle has rarely been subjected to philosophical criticism. The paper objects to it on the ground that it indifferently applies to those cases in which the individuals agree on both their expressed preferences and their reasons for entertaining them, (...) and those cases in which they agree on their expressed preferences, while differing on their reasons. The latter are cases of "spurious unanimity", and it is normatively inappropriate, or so the paper argues, to defend unanimity preservation at the social level for them, so the Pareto principle is formulated much too broadly. The objection seems especially powerful when the principle is applied in an ex ante context of uncertainty, in which individuals can disagree on both their probabilities and utilities, and nonetheless agree on their preferences over prospects. (shrink)

How should an impartial social observer judge distributions of well-being across different individuals when there is uncertainty regarding the state of the world? I explore this question by imposing very weak conditions of rationality and benevolent sympathy on impartial betterness judgments under uncertainty. Although weak enough to be consistent with all the main theories of rationality, these conditions prove to be sufficient to rule out any heterogeneity in what is good for individuals, to require a neutral attitude to uncertainty on (...) the part of the social observer, and to require that both individual and social betterness be strongly separable. (shrink)

Suppose we have a group of Bayesian agents, and suppose that theywould like for their group as a whole to be a Bayesian agent as well. Moreover, suppose that thoseagents want the probabilities and utilities attached to this group agent to be aggregated from theindividual probabilities and utilities in reasonable ways. Two ways of aggregating their individual data areavailable to them, viz., ex ante aggregation and ex post aggregation. The former aggregatesexpected utilities directly, whereas the latter aggregates probabilities and utilities (...) separately.A number of recent formal results show that both approaches have problematic implications. This studydiscusses the philosophical issues arising from those results. In this process, I hope to convincethe reader that these results about Bayesian aggregation are highly significant to decision theorists, butalso of immense interest to theorists working in areas such as ethics and political philosophy. (shrink)

Libertarians believe certain things about rights and responsibilities, about when one person is to be held responsible for invading the rights of another. Libertarians also believe certain things about consent, about when someone should be held to a contract he has entered into. What they don't realize is that the first set of beliefs doesn't mix well with the second set of beliefs—that their intuitions about rights and responsibilities quite simply don't square with their intuitions about consent. Or so I (...) shall be trying to show in this essay. (shrink)

Libertarians believe certain things about rights and responsibilities, about when one person is to be held responsible for invading the rights of another. Libertarians also believe certain things about consent, about when someone should be held to a contract he has entered into. What they don't realize is that the first set of beliefs doesn't mix well with the second set of beliefs—that their intuitions about rights and responsibilities quite simply don't square with their intuitions about consent. Or so I (...) shall be trying to show in this essay. (shrink)

Diversity of opinion both presents problems and aff ords opportunities. Diff erences of opinion can stand in the way of reaching an agreement within a group on what decisions to take. But at the same time, the fact that the differences in question could derive from access to different information or from the exercise of diff erent judgemental skills means that they present individuals with the opportunity to improve their own opinions. This paper explores the implications for solutions to the (...) former (aggregation) problem of supposing that individuals exploit these opportunities. In particular, it argues that rational individual revision of opinion implies that aggregation problems are unstable in a certain sense and that solving them by exploiting the information embedded in individual opinion has profound implications for the conditions that we should impose on aggregation procedures. (shrink)