Procedural mixture sets

Hendrik Rommeswinkel ()
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Hendrik Rommeswinkel: Graduate School of Economics, Hitotsubashi University

Theoretical Economics, Forthcoming

Abstract: This paper provides two variations of the mixture space theorem of Herstein and Milnor (1953). The first replaces the reduction of compound mixtures property with associativity, giving rise to procedural mixture sets in which mixing an element with itself need not return an equivalent element. The second retains standard mixture sets but weakens independence to disjoint independence, restricting it to mixtures whose components have disjoint support. In both cases, the standard axioms of weak order, continuity, and (disjoint) independence yield a mixture entropy representation that contains the Shannon or Tsallis entropy of the mixture weights as a component. We apply the first result to event splitting effects in decisions under risk and the second to deliberate randomization.

Keywords: Decision theory; procedural value; entropy; mixture sets; decision processes; reduction of compound mixtures; associativity (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
Date: 2026-10-06
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