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On the Definition of Objective Probabilities by Empirical Similarity

  • Itzhak Gilboa
  • Offer Lieberman
  • David Schmeidler

We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 843644000000000363.

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Date of creation: 10 Aug 2007
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Handle: RePEc:cla:levrem:843644000000000363
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  1. Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," Levine's Working Paper Archive 391749000000000544, David K. Levine.
  2. Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
  3. Itzhak Gilboa & David Schmeidler & Offer Lieberman, 2006. "Empirical Similarity," Post-Print hal-00746558, HAL.
  4. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2004. "Rationality of Belief," Levine's Bibliography 122247000000000690, UCLA Department of Economics.
  5. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, 07.
  6. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
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