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The Aggregate Excess Demand Function and Other Aggregation Procedures

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  • Donald G. Saari

Abstract

Two theorems are given; the first extends the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set of n (greater than or equal to) 2 commodities to all 2 (superscipt n) minus (n+1) subsets of two or more commodities. The second theorem concerns spatial voting models for k (greater than or equal to) 2 candidates over a space of n issues. The relationships among the sincere election rankings of the candidates for all of the sets of 2 (superscript n) minus1 issues are given. Both theorems have the same kind of conclusion; anything can happen. By showing the mathematical reasons for theses results and by recalling some recent results from statistics, voting, and economics, it is argued that this "anything can happen" conclusion is the type one must anticipate from aggregation procedures; particularly processes of the type commonly used in economic models where the procedure is responsive to changes in agents' preferences, changes in data, etc.

Suggested Citation

  • Donald G. Saari, 1990. "The Aggregate Excess Demand Function and Other Aggregation Procedures," Discussion Papers 908, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:908
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    References listed on IDEAS

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    1. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
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    7. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    8. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
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