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The Instability of Robust Aggregation


  • Hild, Matthias


We discuss the feasibility of Levi's (1990) robust mode of aggregating individuals' evaluations of acts into a social choice function. We examine the process in which we refine decision{theoretic models and account for previously irrelevant parameters of a decision situation (cf. Savage's 'small worlds'). Suppose that, for each individual, we consider a coarse-grained and a fine-grained decision-theoretic model, both of which are consistent with each other in a sense to be defined. We desire any social choice rule to be stable under refinements in the sense that the group choice based on fine-grained individual models and the group choice based on coarse-grained individual models agree for choices among coarse-grained alternatives. We find that any stable robust social choice rule must collapse back into ex ante aggregation. We also provide sufficient conditions, such as Pareto optimality, under which robust aggregation leads to an infinite series of reversals of group choice. For ex ante aggregation, we find that stability is ubiquitous and that it follows from independence of irrelevant alternatives.

Suggested Citation

  • Hild, Matthias, 2001. "The Instability of Robust Aggregation," Working Papers 1113, California Institute of Technology, Division of the Humanities and Social Sciences.
  • Handle: RePEc:clt:sswopa:1113

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    References listed on IDEAS

    1. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, vol. 92(1), pages 35-65, May.
    2. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin expected utility through statewise combinations," Economics Letters, Elsevier, vol. 66(1), pages 49-54, January.
    3. Hong Chew Soo & Karni Edi, 1994. "Choquet Expected Utility with a Finite State Space: Commutativity and Act-Independence," Journal of Economic Theory, Elsevier, vol. 62(2), pages 469-479, April.
    4. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
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