Agreeing to disagree and dilation

Jiji ZHANG, Hailin LIU, Teddy SEIDENFELD

Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)peer-review

Abstract

We consider Geanakoplos and Polemarchakis's generalization of Aumman's famous result on “agreeing to disagree”, in the context of imprecise probability. The main purpose is to reveal a connection between the possibility of agreeing to disagree and the interesting and anomalous phenomenon known as dilation. We show that for two agents who share the same set of priors and update by conditioning on every prior, it is impossible to agree to disagree on the lower or upper probability of a hypothesis unless a certain dilation occurs. With some common topological assumptions, the result entails that it is impossible to agree not to have the same set of posterior probabilities unless dilation is present. This result may be used to generate sufficient conditions for guaranteed full agreement in the generalized Aumman-setting for some important models of imprecise priors, and we illustrate the potential with an agreement result involving the density ratio classes. We also provide a formulation of our results in terms of “dilation-averse” agents who ignore information about the value of a dilating partition but otherwise update by full Bayesian conditioning.

Original languageEnglish
Title of host publicationPMLR: Proceedings of Machine Learning Research
Pages370-381
Number of pages12
Volume62
Publication statusPublished - 2017
Event10th International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2017 - Lugano, Switzerland
Duration: 10 Jul 201714 Jul 2017

Publication series

NamePMLR: Proceedings of Machine Learning Research
ISSN (Print)1938-7228

Conference

Conference10th International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2017
CountrySwitzerland
CityLugano
Period10/07/1714/07/17

Keywords

  • Agreeing to disagree
  • Common knowledge
  • Dilation
  • Imprecise probability

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