TY - JOUR

T1 - Axiomatization of an exponential similarity function

AU - Billot, Antoine

AU - Gilboa, Itzhak

AU - Schmeidler, David

N1 - Funding Information:
We wish to thank Jerome Busemeyer for comments and references. Gilboa, and Schmeidler gratefully acknowledge support from the Polarization and Conflict Project CIT-2-CT-2004-506084 funded by the European Commission-DG Research Sixth Framework Programme. Gilboa and Schmeidler gratefully acknowledge support from the Israel Science Foundation (Grant Nos. 790/00 and 975/03).

PY - 2008/3

Y1 - 2008/3

N2 - 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.

AB - 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.

KW - Axiom

KW - Exponential decay

KW - Similarity function

UR - http://www.scopus.com/inward/record.url?scp=39149090360&partnerID=8YFLogxK

U2 - 10.1016/j.mathsocsci.2007.08.002

DO - 10.1016/j.mathsocsci.2007.08.002

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AN - SCOPUS:39149090360

SN - 0165-4896

VL - 55

SP - 107

EP - 115

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

IS - 2

ER -