Axioms for Measuring without mixing apples and Oranges

Patrick O'Callaghan

MPRA Paper from University Library of Munich, Germany

Abstract: A mixture set is path-connected via a suitable collection of paths, the most common example being a convex set. Yet in many economic settings, there are pairs of prospects that are not connected by a path of mixtures. Consider the thought experiment of von Neumann and Morgenstern involving a glass of milk, a glass of tea and a cup of coffee: we are often asked to choose between convex combinations of milk and tea, yet the same cannot be said of tea and coffee. We introduce partial mixture sets (which need not be path-connected) and provide a formal extension of the well-known axiomatisation of cardinal, linear utility by Herstein and Milnor. We show that partial mixture sets encompass a variety of settings in the literature and present a novel application to cardinal, nonlinear utility on a stochastic process.

Keywords: Utility; Preferences; mixtures (search for similar items in EconPapers)
JEL-codes: C0 C02 D0 D01 (search for similar items in EconPapers)
Date: 2017-09-07
New Economics Papers: this item is included in nep-upt
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