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Inductive Inference: An Axiomatic Approach

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Author Info
Gilboa, I.
Schmeidler, D.

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Abstract

A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of finitely many past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality-case pairs, as follows. Given a memory, each eventuality is ranked according to the sum of the numbers in its row, over cases in memory. The number attached to an eventuality-case pair can be interpreted as the degree of support that the past lends to the plausibility of the eventuality.

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Publisher Info
Paper provided by Tel Aviv in its series Papers with number 2001-19.

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Length: 56 pages
Date of creation: 2001
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Handle: RePEc:fth:teavfo:2001-19

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Keywords: INFERENCE ; EVALUATION ; EXPECTATIONS;

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
D8 - Microeconomics - - Information, Knowledge, and Uncertainty

References listed on IDEAS
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Full references

Cited by:
(explanations, 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.)

  1. Alan Beggs, 2005. "Learning in Bayesian Games with Binary Actions," Economics Series Working Papers 232, University of Oxford, Department of Economics. [Downloadable!]
  2. Massimiliano Amarante, 2006. "Analogical reasoning in decision processes," Discussion Papers 0506-17, Columbia University, Department of Economics. [Downloadable!]
  3. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2003. "Probabilities: Frequencies Viewed in Perspective," Levine's Bibliography 666156000000000295, UCLA Department of Economics. [Downloadable!]
  4. Massimiliano Amarante, 2004. "States, models and unitary equivalence I: Representation theorems and analogical reasoning," Discussion Papers 0405-10, Columbia University, Department of Economics. [Downloadable!]
  5. E. Aragones & I. Gilboa & A. Postlewaite & D. Schmeidler, 2003. "Accuracy vs. Simplicity: A Complex Trade-Off," Levine's Bibliography 506439000000000185, UCLA Department of Economics. [Downloadable!]
    Other versions:
  6. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2004. "Rationality of Belief," Levine's Bibliography 122247000000000690, UCLA Department of Economics. [Downloadable!]
  7. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "Axiomatization of an Exponential Similarity Function," Cowles Foundation Discussion Papers 1485, Cowles Foundation, Yale University. [Downloadable!]
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  8. Massimiliano Amarante, 2006. "States, models and information: A reconsideration of Ellsberg's paradox," Discussion Papers 0506-18, Columbia University, Department of Economics. [Downloadable!]
  9. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2004. "Rationality of Belief Or Why Bayesianism is neither necessary nor sufficient for rationality," PIER Working Paper Archive 04-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
    Other versions:
  10. Stefania D'Amico, 2005. "Density selection and combination under model ambiguity: an application to stock returns," Finance and Economics Discussion Series 2005-09, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  11. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Probabilities as Similarity-Weighted Frequencies," Levine's Bibliography 122247000000000696, UCLA Department of Economics. [Downloadable!]
    Other versions:
  12. David Schmeidler, 2000. "Utility in Case-Based Decision Theory," Working Papers 00-06, Ohio State University, Department of Economics. [Downloadable!]
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  13. Chambers, Christopher P. & Hayashi, Takashi, 2008. "Choice and individual welfare," Working Papers 1286, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  14. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "An Axiomatization of an Exponential Similarity Function," Levine's Bibliography 122247000000000678, UCLA Department of Economics. [Downloadable!]
  15. Voorneveld, M., 2000. "Maximum likelihood equilibria of games with population uncertainty," Discussion Paper 79, Tilburg University, Center for Economic Research. [Downloadable!]
  16. Stefania D'Amico, 2004. "Density Estimation and Combination under Model Ambiguity," Computing in Economics and Finance 2004 273, Society for Computational Economics. [Downloadable!]
  17. VIEILLE, Nicolas & GILBOA, Itzhak, 2002. "Majority vote following a debate," Les Cahiers de Recherche 761, HEC Paris. [Downloadable!]
    Other versions:
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