O'Callaghan, Patrick (2017): Axioms for Measuring without mixing apples and Oranges.

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Abstract
A mixture set is pathconnected 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 pathconnected) and provide a formal extension of the wellknown 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.
Item Type:  MPRA Paper 

Original Title:  Axioms for Measuring without mixing apples and Oranges 
Language:  English 
Keywords:  Utility, Preferences, mixtures 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods D  Microeconomics > D0  General D  Microeconomics > D0  General > D01  Microeconomic Behavior: Underlying Principles 
Item ID:  81196 
Depositing User:  Mr Patrick O'Callaghan 
Date Deposited:  07 Sep 2017 11:46 
Last Modified:  07 Sep 2017 11:47 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/81196 