A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox

Chew, Soo Hong

doi:10.2307/1912052

Cited by 474 publications

(33 citation statements)

References 18 publications

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“…This result-that small probabilities are overweighted and large probabilities are underweighted-is one of the most robust results in risk experiments and has formed the basis for several models (Hong 1983;Kahneman and Tversky 1979). Lattimore, Baker, and Witte (1992) find that probability distortions seem to be dependent on the absolute level of payoffs involved, with higher values yielding a higher point where perceived and actual probabilities are identical.…”

Section: Literature Reviewmentioning

confidence: 66%

Risk Averters that Love Risk? Marginal Risk Aversion in Comparison to a Reference Gamble

Just

Lybbert

2009

American J Agri Economics

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We propose an analytical distinction between standard risk aversion based on the valuation of a single gamble and marginal risk aversion based on the change in valuation between two gambles. We measure marginal risk aversion in two dimensions-mean and variance. Data from a field experiment is used to study marginal risk aversion. Our results suggest that individuals rely on a reference gamble when assessing marginal risk. Individual responses to marginal changes in mean and variance are nearly identical in direction and magnitude-suggesting that information on both standard and marginal risk aversion is needed to accurately model behavior.

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Section: Literature Reviewmentioning

confidence: 66%

Risk Averters that Love Risk? Marginal Risk Aversion in Comparison to a Reference Gamble

Just

Lybbert

2009

American J Agri Economics

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“…Usually, this reversal is explained by distortions of the probabilities in cumulative prospect theory [35,64]. An alternative explanation of the reversal has been proposed in [65] by introducing a non-vanishing weighting function a(x) in a generalized quasi-linear mean model [65][66][67][68] such that the certainty equivalent has the form M a = φ −1 ( dxp(x)a(x)φ(x)/ dxp(x)a(x)). Such a weighting function could also be constructed for the negative free-energy certainty equivalent by defining a generalized difference − F , assuming again β < 0.…”

Section: (B) Application To Allais' Paradoxmentioning

confidence: 99%

Thermodynamics as a theory of decision-making with information-processing costs

2013

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Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here, we propose a thermodynamically inspired formalization of bounded rational decision-making where information processing is modelled as state changes in thermodynamic systems that can be quantified by differences in free energy. By optimizing a free energy, bounded rational decision-makers trade off expected utility gains and information-processing costs measured by the relative entropy. As a result, the bounded rational decision-making problem can be rephrased in terms of well-known variational principles from statistical physics. In the limit when computational costs are ignored, the maximum expected utility principle is recovered. We discuss links to existing decision-making frameworks and applications to human decision-making experiments that are at odds with expected utility theory. Since most of the mathematical machinery can be borrowed from statistical physics, the main contribution is to reinterpret the formalism of thermodynamic free-energy differences in terms of bounded rational decisionmaking and to discuss its relationship to human decision-making experiments.

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“…The disposition effect is part of the general folklore about investing, yet does not arise within the standard neoclassical framework. Indeed, it does not even appear in the alternative positive theories of decisionmaking under uncertainty (Machina [19], Chew [4], and Chew and MacCrimmon [5]).…”

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confidence: 99%

The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence

Shefrin¹,

Statman²

1985

The Journal of Finance

1,043

1,083

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One of the most significant and unique features in Kahneman and Tversky's approach to choice under uncertainty is aversion to loss realization. This paper is concerned with two aspects of this feature. First, we place this behavior pattern into a wider theoretical framework concerning a general disposition to sell winners too early and hold losers too long. This framework includes other elements, namely mental accounting, regret aversion, self-control, and tax considerations. Second, we discuss evidence which suggests that tax considerations alone cannot explain the observed patterns of loss and gain realization, and that the patterns are consistent with a combined effect of tax considerations and the three other elements of our framework. We also show that the concentration of loss realizations in December is not consistent with fully rational behavior, but is consistent with our theory. IT HAS BEEN WELL-KNOWN for over thirty years that individual decision makers do not behave in accordance with the axioms of expected utility theory. The famous Allais paradoxes [1] have made this point abundantly clear. Recent work by Kahneman and Tversky [15], Machina [19], and others has sought to provide a theory which describes how decision makers actually behave when confronted with choice under uncertainty. One of the key findings by Kahneman and Tversky concerns decision makers whose recent gambling history reflects losses. They indicate that their analysis suggests that a person who has not made peace with his losses is likely to accept gambles that would be unacceptable to him otherwise (p. 287).Kahneman and Tversky's finding was obtained in a controlled experimental situation. Economists tend to treat experimental evidence with some caution and are reluctant to conclude automatically that similar features will be exhibited in real-world market settings. Indeed, it is important to look at market behavior in order to ascertain whether such behavior patterns can be discerned in actual trading.In this paper, we examine decisions to realize gains and losses in a market setting. Specifically, we focus attention on financial markets and seek to determine whether investors exhibit a reluctance to realize losses (disposition to "ride * University of Santa Clara, Leavey School of Business. We would like to acknowledge the helpful remarks made on earlier versions by

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A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox

Cited by 474 publications

References 18 publications

Risk Averters that Love Risk? Marginal Risk Aversion in Comparison to a Reference Gamble

Risk Averters that Love Risk? Marginal Risk Aversion in Comparison to a Reference Gamble

Thermodynamics as a theory of decision-making with information-processing costs

The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence

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