Acceptance, Aggregation and Scoring Rules
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As the ongoing literature on the paradoxes of the Lottery and the Preface reminds us, the nature of the relation between probability and rational acceptability remains far from settled. This article provides a novel perspective on the matter by exploiting a recently noted structural parallel with the problem of judgment aggregation. After offering a number of general desiderata on the relation between finite probability models and sets of accepted sentences in a Boolean sentential language, it is noted that a number of these constraints will be satisfied if and only if acceptable sentences are true under all valuations in a distinguished non-empty set W. Drawing inspiration from distance-based aggregation procedures, various scoring rule based membership conditions for W are discussed and a possible point of contact with ranking theory is considered. The paper closes with various suggestions for further research.
I am grateful to the members of the Formal Epistemology Project, KU Leuven, and to the audience of PROGIC 2009, Groningen for useful feedback on earlier versions of this paper. I am also indebted to two anonymous referees for this journal for the time and trouble that they took to provide exceptionally detailed and insightful reports. The work carried out by one of these referees, in particular, went way beyond the call of duty. Part of the research for this article was funded by a Research Foundation—Flanders (FWO) postdoctoral research grant.