Jan Sprenger

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to such a problem as the \textit{discursive dilemma}. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how good the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group-external decision-making, respectively. We compare those methods in a probabilistic model, demonstrate the robustness of our results over various generalizations and discuss their applicability in different situations. The findings vindicate (i) that in judgment aggregation problems, reasons should carry higher weight than conclusions and (ii) that considering members of an advisory board to be highly competent is a better strategy than to underestimate their advice.".

Abductive reasoning assigns special status to the explanatory power of a hypothesis. But how do people make explanatory judgments? Our study clarifies this issue by asking: How does the explanatory power of a hypothesis cohere with other cognitive factors? How does probabilistic information affect explanatory judgments? In order to answer these questions, we conducted an experiment with 671 participants. Their task was to make judgments about a potentially explanatory hypothesis and its cognitive virtues. In the responses, we isolated three constructs: Explanatory Value, Rational Acceptability, and Entailment. Explanatory judgments strongly cohered with judgments of causal relevance and with a sense of understanding. Furthermore, we found that Explanatory Value was sensitive to manipulations of statistical relevance relations between hypothesis and evidence, but not to explicit information about the prior probability of the hypothesis. These results indicate that probabilistic information about statistical relevance is a strong determinant of Explanatory Value. More generally, our study suggests that abductive and probabilistic reasoning are two distinct modes of inference.

This paper focuses on the question of how to resolve disagreement and uses the Lehrer-Wagner model as a formal tool for investigating consensual decision-making. The main result consists in a general definition of when agents treat each other as epistemic peers (Kelly 2005; Elga 2007), and a theorem vindicating the “equal weight view” to resolve disagreement among epistemic peers. We apply our findings to an analysis of the impact of social network structures on group deliberation processes, and we demonstrate their stability with the help of numerical simulations.

To what extent does the design of statistical experiments, in particular sequential trials, affect their interpretation? Should postexperimental decisions depend on the observed data alone, or should they account for the used stopping rule? Bayesians and frequentists are apparently deadlocked in their controversy over these questions. To resolve the deadlock, I suggest a three‐part strategy that combines conceptual, methodological, and decision‐theoretic arguments. This approach maintains the pre‐experimental relevance of experimental design and stopping rules but vindicates their evidential, postexperimental irrelevance. †To contact the author, please write to: Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands; e‐mail: [email protected]

This paper explores the scope and limits of rational consensus through mutual respect, with the primary focus on the best known formal model of consensus: the Lehrer–Wagner model. We consider various arguments against the rationality of the Lehrer–Wagner model as a model of consensus about factual matters. We conclude that models such as this face problems in achieving rational consensus on disagreements about unknown factual matters, but that they hold considerable promise as models of how to rationally resolve non-factual disagreements.