Projects per year
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.
|Title of host publication||PMLR: Proceedings of Machine Learning Research|
|Number of pages||12|
|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
|Name||PMLR: Proceedings of Machine Learning Research|
|Conference||10th International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2017|
|Period||10/07/17 → 14/07/17|
- Agreeing to disagree
- Common knowledge
- Imprecise probability
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- 1 Finished
Causation, Decision, and Imprecise Probabilities
ZHANG, J. & SEIDENFELD, T.
Research Grants Council (HKSAR)
1/01/16 → 31/12/17
Project: Grant Research