Axiomatization of an exponential similarity function
Journal article: 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.
Author(s)
Antoine Billot, Itzhak Gilboa, David Schmeidler
Journal
- Mathematical Social Sciences
Date of publication
- 2008
Keywords
- Similarity function
- Axiom
- Exponential decay
Pages
- pp.107-115
URL of the HAL notice
Version
- 1
Volume
- Vol.55,n°2