The Algebraic versus the Topological Approach to Additive Representations
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It is proved that, under a nontriviality assumption, an additive function on a Cartesian product of connected topological spaces is continuous, whenever the preference relation, represented by this function, is continuous. The result is used to generalize a theorem of Debreu ((1960). Mathematical methods in the social sciences (pp. 16–26). Stanford: Stanford Univ. Press) on additive representations and to argue that the algebraic approach of KLST to additive conjoint measurement is preferable to the more customary topological approach. Applications to the representation of strength of preference relations and to the characterization of subjective expected utility maximization are given.
- topological approach
- preference relation