The paper presents a method for lottery valuation using the relative utility function, which resembles the utility curve proposed by Markowitz (1952a). The paper discusses lotteries with discrete and continuous outcome distributions as well as lotteries with positive, negative and mixed outcomes. The solution is similar to the Expected Utility Theory approach and does not use the probability weighting function. Solutions to several classical behavioral problems, including the Allais paradox, are presented, demonstrating that the method can be used for valuing lotteries even in more complex cases of outcomes described by a combination of Beta distributions.(original abstract)
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The paper presents a method for lottery valuation using the relative utility function. This function was presented by Kontek (2009) as "the aspiration function" and resembles the utility curve proposed by Markowitz (1952A). The paper discusses lotteries with discrete and continuous outcome distributions as well as lotteries with positive, negative and mixed outcomes providing analytical formulas for certainty equivalents in each case. The solution is similar to the Expected Utility Theory approach and does not use the probability weighting function - one of the key elements of Prospect Theory. Solutions to several classical behavioral problems, including the Allais paradox, are presented, demonstrating that the method can be used for valuing lotteries even in more complex cases of outcomes described by a combination of Beta distributions. The paper provides strong arguments against Prospect Theory as a model for describing human behavior and lays the foundations for Relative Utility Theory - a new theory of decision making under conditions of risk. (original abstract)
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W artykule przedstawiono wybrane z literatury przedmiotu eksperymenty związane z paradoksem Allais. Przegląd tych eksperymentów miał na celu prezentację samego paradoksu oraz związanego z nim efektu pewności, efektu wspólnych konsekwencji i efektu wspólnego czynnika. Omówione zostały również wybrane sposoby redukcji stopnia naruszenia zasad teorii oczekiwanej użyteczności. (fragment tekstu)
EN
Theorems about the rational decision making play very important role in the decision theory. According to these theorems people make their decisions by using the rule about maximum benefits. However in the literature we can find conclusions from research and experiments which indicate that when people are making decisions, they are very often breaking that rule about maximum profits. According to that research a few paradoxes of rationality were formulated. In this article experiments concerning the Allais paradoxes are analyzed. The incompatibility between paradox and the expected utility theory were discussed. Also the certainty effect and the common consequence effect were analyzed. (original abstract)
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The paper presents a method for lottery valuation using the relative utility function. This function was presented by Kontek (2009) as "the aspiration function" and resembles the utility curve proposed by Markowitz (1952A). The paper discusses lotteries with discrete and continuous outcome distributions as well as lotteries with positive, negative and mixed outcomes providing analytical formulas for certainty equivalents in each case. The solution is similar to the Expected Utility Theory approach and does not use the probability weighting function - one of the key elements of Prospect Theory. Solutions to several classical behavioral problems, including the Allais paradox, are presented, demonstrating that the method can be used for valuing lotteries even in more complex cases of outcomes described by a combination of Beta distributions. The paper provides strong arguments against Prospect Theory as a model for describing human behavior and lays the foundations for Relative Utility Theory - a new theory of decision making under conditions of risk.(original abstract)
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This paper introduces the concept of range-dependent utility. Instead of reference dependence which evaluates outcomes relative to some reference point, we postulate dependence on a given lottery (set of lotteries) outcomes range. In this way the decision maker is a fully rational expected utility maximizer only within a certain range. Range-dependent utility enables experimental results to be explained without recourse to the probability weighting function. Experimental data show that range-dependent utilities can be normalized to obtain decision utility - a single utility function able to describe decisions involving lotteries defined over different ranges. Both the data analysis as well as theoretical considerations concerning monotonicity indicate that the decision utility should be of S-shape. (original abstract)
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