Almost Everybody Disagrees Almost All the Time: The Genericity of Weakly Merging Nowhere
AbstractSuppose we randomly pull two agents from a population and ask them to observe an unfolding, infinite sequence of zeros and ones. If each agent starts with a prior belief about the true sequence and updates this belief on revelation of successive observations, what is the chance that the two agents will come to agree on the likelihood that the next draw is a one? In this paper we show that there is no chance. More formally, we show that under a very unrestrictive definition of what it means to draw priors "randomly," the probability that two priors have any chance of weakly merging is zero. Indeed, almost surely, the two measures will be singular--one prior will think certain a set of sequences that the other thinks impossible, and vice versa. Our result is meant as a critique of the "rational learning" literature, which seeks positive convergence results on infinite product spaces by augmenting the process of Bayesian updating with seeming regularity conditions, variously labeled "consistency" or "compatibility" assumptions. Our object is to investigate just how regular these assumption and results are when considered in the space of all possible prior distributions. Our results on the genericity of nowhere weak merging and singularity speak not just to the specific assumptions and results that appear in the literature, but to the "rational learning" approach generally. We call instead for a different approach to learning, one that recognizes the necessity of genuine, substantive restrictions on beliefs and proposes "extra rational" restrictions that are explicitly grounded in our best understanding of human behavior, ideally gleaned from experimental data.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University of Pennsylvania Law School in its series Scholarship at Penn Law with number upenn_wps-1001.
Date of creation:
Date of revision:
Contact details of provider:
Web page: http://www.law.upenn.edu/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-08-02 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ehud Kalai & Ehud Lehrer, 1990.
"Rational Learning Leads to Nash Equilibrium,"
925, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University.
- E. Kalai & E. Lehrer, 2010. "Rational Learning Leads to Nash Equilibrium," Levine's Working Paper Archive 529, David K. Levine.
- Miller, Ronald I. & Sanchirico, Chris William, 1999. "The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 170-190, October.
- Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
- Dean Foster & H Peyton Young, 1999.
"On the Impossibility of Predicting the Behavior of Rational Agents,"
Economics Working Paper Archive
423, The Johns Hopkins University,Department of Economics, revised Jun 2001.
- Dean P. Foster & H. Peyton Young, 2001. "On the Impossibility of Predicting the Behavior of Rational Agents," Working Papers 01-08-039, Santa Fe Institute.
- Arnoud W.A. Boot & Anjan V. Thakor, 2003.
"The Economic Value of Flexibility when there is Disagreement,"
Tinbergen Institute Discussion Papers
03-002/2, Tinbergen Institute.
- Boot, Arnoud W A & Thakor, Anjan, 2003. "The Economic Value of Flexibility When There is Disagreement," CEPR Discussion Papers 3709, C.E.P.R. Discussion Papers.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
If references are entirely missing, you can add them using this form.