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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 Aummansetting 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 “dilationaverse” agents who ignore information about the value of a dilating partition but otherwise update by full Bayesian conditioning.
Original language  English 

Title of host publication  PMLR: Proceedings of Machine Learning Research 
Pages  370381 
Number of pages  12 
Volume  62 
Publication status  Published  2017 
Event  10th International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2017  Lugano, Switzerland Duration: 10 Jul 2017 → 14 Jul 2017 
Publication series
Name  PMLR: Proceedings of Machine Learning Research 

ISSN (Print)  19387228 
Conference
Conference  10th International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2017 

Country/Territory  Switzerland 
City  Lugano 
Period  10/07/17 → 14/07/17 
Keywords
 Agreeing to disagree
 Common knowledge
 Dilation
 Imprecise probability
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 1 Finished

Causation, Decision, and Imprecise Probabilities
ZHANG, J. (PI) & SEIDENFELD, T. (CoI)
Research Grants Council (HKSAR)
1/01/16 → 31/12/17
Project: Grant Research