Axiomatization of an exponential similarity function

Antoine Billot, Itzhak Gilboa*, David Schmeidler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

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.

Original languageEnglish
Pages (from-to)107-115
Number of pages9
JournalMathematical Social Sciences
Volume55
Issue number2
DOIs
StatePublished - Mar 2008

Funding

FundersFunder number
European Commission-DG Research Sixth Framework Programme
Israel Science Foundation790/00, 975/03

    Keywords

    • Axiom
    • Exponential decay
    • Similarity function

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