THE STRUCTURE OF UTILITY FUNCTIONS.
STANFORD UNIV CALIF INST FOR MATHEMATICAL STUDIES IN THE SOCIAL SCIENCES
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A continuous complete preference ordering is defined on an arcconnected, topologically separable product space S S1xS2x..xSn. Call 1,..n sectors and say that a set A of sectors is separable if the conditional ordering on A, given what happens off it, is independent of the latter, essential if it matters what happens on A, at least sometimes, and strictly essential if it always does. It is shown how to determine the structure of the utility function, given a collection of separable sets, when each sector is strictly essential. Various examples are discussed, an alternative approach sketched, and, finally, the requirement of strict essentiality replaced by the basically nugatory condition that each sector be essential. The results can, of course, be applied to other functions, too. Author
- Operations Research