Axiomatization of an Exponential Similarity Function

Antoine Billot, Itzhak Gilboa and David Schmeidler

No 1485, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: An agent is asked to assess a real-valued variable y based on certain characteristics x=(x^{1},...,x^{m}), and on a database consisting of n observations of (x^{1},...,x^{m},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, y_{n+1}^{s}, be the weighted average of all previously observed values y_{i}, where the weight of y_{i} is the similarity between the vector x_{n+1}^{1},...,x_{n+1}^{m}, associated with y_{n+1}, and the previously observed vector, x_{i}^{1},...,x_{i}^{m}. This paper axiomatizes, in terms of the prediction y_{n+1}, a similarity function that is a (decreasing) exponential in a norm of the difference between the two vectors compared.

Keywords: Similarity; exponential (search for similar items in EconPapers)
JEL-codes: C8 D8 (search for similar items in EconPapers)
Pages: 10 pages
Date: 2004-09
New Economics Papers: this item is included in nep-hpe
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Published in Mathematical Social Sciences (2008), 55: 107-115

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Related works:
Chapter: Axiomatization of an Exponential Similarity Function (2012)
Journal Article: Axiomatization of an exponential similarity function (2008)
Working Paper: Axiomatization of an exponential similarity function (2008)
Working Paper: Axiomatization of an exponential similarity function (2008)
Working Paper: An Axiomatization of an Exponential Similarity Function (2004)
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