 Axiomatization of an exponential similarity functionAntoine Billot, Itzhak Gilboa and David Schmeidler Mathematical Social Sciences, 2008, vol. 55, issue 2, 107-115 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. Date: 2008 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:55:y:2008:i:2:p:107-115 Access Statistics for this article Mathematical Social Sciences is currently edited by J.-F. Laslier More articles in Mathematical Social Sciences from Elsevier |
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