What is it about?
What makes people buy lotteries and insure their property? We believe that it is the range of possible outcomes. While buying a lottery ticket costs almost nothing, hitting the jackpot may change your life completely. On the other hand your house insurance premium is probably low compared to the possible loss in case your house is left unprotected. We develop the range-dependent utility model: a model of decision-making under risk in which people's preferences depend on the range of possible outcomes in a given risky prospect.
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Why is it important?
The range-dependent model explains many experimentally documented preference patterns that are inconsistent with the standard Expected Utility model. Contrary to other models that also explain similar phenomena our model is not based on probability weighting and rank dependence (small probabilities of extreme events are overweighted, probabilities of intermediate events are underweighted); the concepts which are mathemathically elegant but psychologically unintuitive. On the other hand, the range-dependent utility model is based on range effects: the psychologically well-justified concept introduced by Parducci, 1965 (Range-Frequency Theory) that has been extensively studied in psychophysics and psychology.
Perspectives
Writing this article was a lot of fun. The original idea of applying the idea of range-dependence to risky decisions needed to be properly formalized and axiomatized. This was my job and I enjoyed the time I spent proving the main results of the paper. On the way me and Krzysztof had a lot of opportunities to meet and discuss with some great scholars whose ideas influenced us considerably such as: Allen Parducci - founding father of Range-Frequency Theory as well as co-inventor of windsurfing that is my passion for at least 10 years, Mark Machina - whose concern with monotonicity and continuity has taken almost 9 months untill a proper theorem was proved (Theorem 3 in the paper), Harry Markowitz - probably the first one to realize that utility should be of S-shape (Markowitz, 1952) and who believes that talking to a Samsung Galaxy is just as much fun as it is with an iPhone, Manel Baucells - who has accepted our paper for publication in Management Science and started collaborating with us on a project that combines ideas of range-dependent utility model and probability and time trade-off (Baucells, Heukamp, 2012).
Dr Michal Lewandowski
Warsaw School of Economics
The first time I came up with the idea of this paper was as early as in 2008. The first person who liked this idea was Harry Markowitz, the 1990 Nobel Prize Winner in Economics, who hypothesized a double S-shaped utility function in his 1952 "Utility of Wealth" paper. Then it took several years of hard work with Michal (and many rejections on the way) to finally get the shape that was accepted by Management Science. Although the paper is very mathematical (many axioms, theorems, proofs) the basic idea is very simple: people evaluate risky prospects relative to the maximal gain and maximal loss. Enjoy reading!
Dr Krzysztof Kontek
Warsaw School of Economics
Read the Original
This page is a summary of: Range-Dependent Utility, Management Science, June 2017, INFORMS,
DOI: 10.1287/mnsc.2017.2744.
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