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)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...) We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

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)

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 first section of this paper asks why the notion of consensus has recently come to the fore in the medical humanities, and suggests that the answer is a function of growing technological and professional complexity. The next two sections examine the concept of consensus analytically, citing some of the recent philosophical literature. The fourth section looks at committee deliberations and their desirable outcomes, and questions the degree to which consensus serves those outcomes. In the fifth and last section it (...) is suggested that if I am to subscribe to a consensual outcome responsibly I must be personally committed to it, and that this requires a form of knowledge I call ‘fiduciary’, in this case knowledge of the competence and trustworthiness of other participants in deliberation whose expertise may have influenced my agreement. (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)

Robert Fogelin has argued that in deep disagreements, resolution cannot be achieved by rational argumentation. In response, Richard Feldman has claimed that deep disagreements can be resolved in a similar way to more everyday disagreements. I argue that Feldman’s claim is based on a relatively superficial notion of “resolution” of a disagreement whereas the notion at stake in Fogelin’s argument is more substantive. Furthermore, I argue that Feldman’s reply is based on a particular reading of Fogelin’s argument. There is an (...) alternative reading, which takes the central concern to be the role of common ground in argumentation. Engaging with this version of Fogelin’s argument is also a worthwhile endeavour. (shrink)

Philosophers have often noted that science displays an uncommon degree of consensus on beliefs among its practitioners. Yet consensus in the sciences is not a goal in itself. I consider cases of consensus on beliefs as concrete events. Consensus on beliefs is neither a sufficient nor a necessary condition for presuming that these beliefs constitute knowledge. A concrete consensus on a set of beliefs by a group of people at a given historical period may be explained by different factors according (...) to various hypotheses. A particularly interesting hypothesis from an epistemic perspective is the knowledge hypothesis: shared knowledge explains a consensus on beliefs. If all the alternative hypotheses to the knowledge hypotheses are false or are not as good in explaining a concrete consensus on beliefs, the knowledge hypothesis is the best explanation of the consensus. If the knowledge hypothesis is best, a consensus becomes a plausible, though fallible, indicator of knowledge. I argue that if a consensus on beliefs is uncoerced, uniquely heterogeneous and large, the gap between the likelihood of the consensus given the knowledge hypothesis and its likelihoods given competing hypotheses tends to increase significantly. Consensus is a better indicator of knowledge than "success" or "human flourishing". (shrink)

A traditional proposition in the philosophy and the sociology of science wants that consensus between specialists of a scientific discipline is a reliable indicator of their access to genuine knowledge. In an interesting reassessment of this principle, Aviezer Tucker has analyzed the implications and the significance of this thesis in relation to historical research, and has established that parts of the historiographical community that display high degrees of consensus among their practitioners can be described in terms of the same relationship (...) existing in empirical sciences between the exemplification of significant level of agreement and shared knowledge. After a concise summary of Tucker’s general view of the relationship between consensus and knowledge and an analysis of its discussion by Boaz Miller, this paper proposes a critical discussion of the limits and the virtues of this approach and concludes that it is possible to assume that a theory of the sort outlined by Tucker and Miller may describe in an exhaustive way the dynamics of the consensual communities only after some important caveats and integrations. In the closing section, a brief review of Tucker’s picture of historiographical consensus will be proposed. (shrink)