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Axiomatization of an exponential similarity function

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  • Billot, Antoine
  • Gilboa, Itzhak
  • Schmeidler, David

Abstract

An individual is asked to assess a real-valued variable y based on certain characteristics x = (x1,..., xm), and on a database consisting of n observations of (x1,..., xm, y). A possible approach to combine past observations of x and y with the current values of x to generate an assessment of y is similarity-weighted averaging. It suggests that the predicted value of y, yn+1s, be the weighted average of all previously observed values yi, where the weight of yi is the similarity between the vector xn+11,..., xn+1m, associated with yn+1, and the previously observed vector, xi1,..., xim. This paper axiomatizes, in terms of the prediction yn+1, a similarity function that is a (decreasing) exponential in a norm of the difference between the two vectors compared.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 55 (2008)
Issue (Month): 2 (March)
Pages: 107-115

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Handle: RePEc:eee:matsoc:v:55:y:2008:i:2:p:107-115

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Web page: http://www.elsevier.com/locate/inca/505565

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  1. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Probabilities as Similarity-Weighted Frequencies," Levine's Bibliography 122247000000000696, UCLA Department of Economics.
  2. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
  3. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
  4. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2003. "Probabilities: Frequencies Viewed in Perspective," Levine's Bibliography 666156000000000295, UCLA Department of Economics.
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Cited by:
  1. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
  2. Pape, Andreas Duus & Kurtz, Kenneth J., 2013. "Evaluating case-based decision theory: Predicting empirical patterns of human classification learning," Games and Economic Behavior, Elsevier, vol. 82(C), pages 52-65.
  3. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004. "Empirical Similarity," Levine's Bibliography 122247000000000684, UCLA Department of Economics.
  4. Pape, Andreas & Kurtz, Kenneth, 2013. "Evaluating Case-based Decision Theory: Predicting Empirical Patterns of Human Classification Learning (Extensions)," MPRA Paper 45206, University Library of Munich, Germany.
  5. Wolfgang Ossadnik & Dirk Wilmsmann & Benedikt Niemann, 2013. "Experimental evidence on case-based decision theory," Theory and Decision, Springer, vol. 75(2), pages 211-232, August.
  6. Gilboa, Itzhak & Lieberman, Offer & Schmeidler, David, 2011. "A similarity-based approach to prediction," Journal of Econometrics, Elsevier, vol. 162(1), pages 124-131, May.
  7. Antoine Billot & Itzhak Gilboa & David Schmeidler & Dov Samet, 2004. "Probabilities as Similarity-Weighted Frequencies," Cowles Foundation Discussion Papers 1492, Cowles Foundation for Research in Economics, Yale University.
  8. Golosnoy, Vasyl & Hamid, Alain & Okhrin, Yarema, 2014. "The empirical similarity approach for volatility prediction," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 321-329.
  9. Gayer, Gabrielle, 2010. "Perception of probabilities in situations of risk: A case based approach," Games and Economic Behavior, Elsevier, vol. 68(1), pages 130-143, January.

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