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On the statistical foundations of non-linear utility theory: The case of status quo-dependent preferences
Institution:1. Division of Marine Environment & Bioscience, Korea Maritime and Ocean University, Busan 606-791, South Korea;2. Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Japan;3. Geological Survey of Japan, AIST, Japan;1. CNRS, Université de Lorraine, CREGU, UMR 7359 GeoRessources, BP 70239, Vandœuvre-lès-Nancy F-54506, France;2. CNRS, Université de Lorraine, UMR 7360 LIEC, Vandœuvre-lès-Nancy F-54506, France;3. CNRS, Université de Lorraine, UMR 7274 LRGP, Nancy F-54001, France;1. Institute of Soil and Water Conservation, Northwest A&F University, Yangling, Shaanxi, China;2. Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling, Shaanxi, China;3. Department of Soil Science, University of Saskatchewan, Saskatoon, Canada;4. Research Institute for Geo-Hydrological Protection, National Research Council, Perugia, Italy;1. National Council for Air and Stream Improvement, Inc., 1258 Windemere Avenue, Naperville, IL 60564, USA;2. National Council for Air and Stream Improvement, Inc., PO Box 340317, Clemson, SC 29634, USA
Abstract:An account of non-expected utility is given which resumes concepts of μσ-analysis from statistical decision theory and combines them with standard principles of preference theory such as weak order, continuity and stochastic dominance. A three-parameter family of probability-dependent utility functions is specified, which is governed by the decision maker's aspiration level, distribution of present wealth, or status quo, and discount parameter for future risks. The approach offers a simple resolution of the Allais Paradox and explains basic patterns of probability-dependent risk attitudes arising in theoretical and applied decision analysis.
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