Title

Agreeing to disagree and dilation

Document Type

Journal article

Source Publication

PMLR: Proceedings of Machine Learning Research

Publication Date

2017

Volume

62

First Page

370

Last Page

381

Keywords

agreeing to disagree, common knowledge, dilation, imprecise probability

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.

E-ISSN

19387228

Funding Information

This research was supported by the Research Grants Council of Hong Kong under the General Research Fund LU13600715, and by a Faculty Research Grant from Lingnan University. {LU13600715}

Publisher Statement

Copyright © PMLR 2017. All rights reserved. Access to external full text or publisher's version may require subscription.

Full-text Version

Publisher’s Version

Language

English

Recommended Citation

Zhang, J., Liu, H. & Seidenfeld, T. (2017). Agreeing to disagree and dilation. PMLR: Proceedings of Machine Learning Research, 62, 370-381.

Share

COinS