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Pavlo R Blavatskyy - One of the best experts on this subject based on the ideXlab platform.

  • a probability weighting function for cumulative prospect theory and mean gini approach to optimal portfolio investment
    2013
    Co-Authors: Pavlo R Blavatskyy
    Abstract:

    This paper presents a new two-parameter probability weighting function for Tversky and Kahneman (1992) cumulative prospect theory as well as its special cases — Quiggin (1981) rank-dependent utility and Yaari (1987) dual model. The proposed probability weighting function can be inverse S-shaped (concave near probability zero and convex near probability one), S-shaped, globally convex and globally concave. Utility function of Yaari (1987) dual model with the proposed probability weighting function is a linear tradeoff between the lottery’s expected value (i.e. the first L-moment), Gini (1912) mean difference statistic (or the second L-moment, known as L-scale) and the third L-moment (measuring the lottery’s skewness). Two parameters of the proposed probability weighting function can be interpreted as a decision maker’s sensitivity to the dispersion and skewness of lottery’s outcomes. A decision maker who prefers positively skewed distributions (e.g., a small chance to win a highly desirable outcome) and dislikes negatively skewed distributions generally has an inverse S-shaped probability weighting function. This function crosses the 45° line at a probability smaller (greater) than 0.5 if a decision maker is also averse (attracted) to the dispersion of outcomes. Cumulative prospect theory with our proposed probability weighting function can Rationalize the Common Ratio effect (i.e. a systematic fanning-out of indifference curves) in one type of Common Ratio problems as well as the reverse Common Ratio effect (i.e. a systematic fanning-in) — in another type of Common Ratio problems, in accordance with the recent experimental evidence.

  • probabilistic choice and stochastic dominance
    Economic Theory, 2012
    Co-Authors: Pavlo R Blavatskyy
    Abstract:

    This paper presents an axiomatic model of probabilistic choice under risk. In this model, when it comes to choosing one lottery over another, each alternative has a chance of being selected, unless one lottery stochastically dominates the other. An individual behaves as if he or she compares lotteries to a reference lottery—the least upper bound or the greatest lower bound in terms of stochastic dominance. The proposed model is compatible with several well-known violations of expected utility theory such as the Common Ratio effect and the violations of betweenness. Necessary and sufficient conditions for the proposed model are completeness, weak stochastic transitivity, continuity, Common consequence independence, outcome monotonicity, and odds Ratio independence.

  • probabilistic choice and stochastic dominance
    Social Science Research Network, 2008
    Co-Authors: Pavlo R Blavatskyy
    Abstract:

    This paper presents an axiomatic model of probabilistic choice under risk. In this model, when it comes to choosing one lottery over another, each alternative has a chance of being selected, unless one lottery stochastically dominates the other. An individual behaves as if he compares lotteries to a reference lottery - a least upper bound or a greatest lower bound in terms of weak dominance. The proposed model is compatible with several well-known violations of expected utility theory such as the Common Ratio effect and the violations of the betweenness. Necessary and sufficient conditions for the proposed model are completeness, weak stochastic transitivity, continuity, Common consequence independence, outcome monotonicity, and odds Ratio independence.

  • stochastic expected utility theory
    Journal of Risk and Uncertainty, 2007
    Co-Authors: Pavlo R Blavatskyy
    Abstract:

    This paper proposes a new decision theory of how individuals make random errors when they compute the expected utility of risky lotteries. When distorted by errors, the expected utility of a lottery never exceeds (falls below) the utility of the highest (lowest) outcome. This assumption implies that errors are likely to overvalue (undervalue) lotteries with expected utility close to the utility of the lowest (highest) outcome. Proposed theory explains many stylized empirical facts such as the fourfold pattern of risk attitudes, Common consequence effect (Allais paradox), Common Ratio effect and violations of betweenness. Theory fits the data from ten well-known experimental studies at least as well as cumulative prospect theory.

Drazen Prelec - One of the best experts on this subject based on the ideXlab platform.

  • the probability weighting function
    Econometrica, 1998
    Co-Authors: Drazen Prelec
    Abstract:

    A probability weighting finction w(p) is a prominent feature of several non-expected utility theories, including prospect theoiy and rank-dependent models. Empirical esti- mates indicate that w(p) is regressive (first w(p)>p, then iv(p)Common-Ratio EFFECT (Allais (1953)) refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects. Thus a person who prefers a sure gain of $100,000 over a coin toss for $300,000 or nothing, might also prefer a one-in-a-million lottery ticket for $300,000 over a two-in-a-million lottery ticket for $100,000. This contradicts expected utility but not Common sense: There is a world of difference between certainty and a 50-50 shot; the difference between one or two chances in a million is negligible. The example has all the force and simplicity of classical arguments for nonlinear utility, where the utility interval from, say $10 and $20, is taken as self-evidently greater than the utility interval from $1,000,010 and $1,000,020. Both arguments appeal directly to our intuitions about numbers. A major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability Ratio. A minor difference is that in the money domain a constant interval has less impact as the numbers get larger, while in the probability domain a constant Ratio has less impact as the numbers get smaller. Putting the two demonstRations side by side like this raises an interesting question, namely, whether an account of nonlinearity-in-probabilities can be somehow adapted from classical utility theory (modulo a log transformation, converting statements about probability Ratios into statements about utility intervals). Indeed, in their seminal paper on prospect theory, Kahneman and Tversky (1979) explained the Common-Ratio effect by means of a nonlinear transformation of probabilities into "decision weights," p -* w(p), with log(w)

Ido Erev - One of the best experts on this subject based on the ideXlab platform.

  • small feedback based decisions and their limited correspondence to description based decisions
    Journal of Behavioral Decision Making, 2003
    Co-Authors: Greg Barron, Ido Erev
    Abstract:

    The present paper explores situations in which the information available to decision makers is limited to feedback concerning the outcomes of their previous decisions. The results reveal that experience in these situations can lead to deviations from maximization in the opposite direction of the deviations observed when the decisions are made based on a description of the choice problem. Experience was found to lead to a reversed Common Ratio/certainty effect, more risk seeking in the gain than in the loss domain, and to an underweighting of small probabilities. Only one of the examined properties of description-based decisions, loss aversion, seems to emerge robustly in these ‘feedback-based’ decisions. These results are summarized with a simple model that illustrates that all the unique properties of feedback-based decisions can be a product of a tendency to rely on recent outcomes. Copyright # 2003 John Wiley & Sons, Ltd.

Greg Barron - One of the best experts on this subject based on the ideXlab platform.

  • small feedback based decisions and their limited correspondence to description based decisions
    Journal of Behavioral Decision Making, 2003
    Co-Authors: Greg Barron, Ido Erev
    Abstract:

    The present paper explores situations in which the information available to decision makers is limited to feedback concerning the outcomes of their previous decisions. The results reveal that experience in these situations can lead to deviations from maximization in the opposite direction of the deviations observed when the decisions are made based on a description of the choice problem. Experience was found to lead to a reversed Common Ratio/certainty effect, more risk seeking in the gain than in the loss domain, and to an underweighting of small probabilities. Only one of the examined properties of description-based decisions, loss aversion, seems to emerge robustly in these ‘feedback-based’ decisions. These results are summarized with a simple model that illustrates that all the unique properties of feedback-based decisions can be a product of a tendency to rely on recent outcomes. Copyright # 2003 John Wiley & Sons, Ltd.

Zacharias Maniadis - One of the best experts on this subject based on the ideXlab platform.

  • An Approximate Dual-Self Model and Paradoxes of Choice Under Risk
    Journal of Economic Psychology, 2014
    Co-Authors: Drew Fudenberg, David K. Levine, Zacharias Maniadis
    Abstract:

    We derive a simplified version of the model of Fudenberg and Levine [2006, 2011] and show how this approximate model is useful in explaining choice under risk. We show that in the simple case of three outcomes, the model can generate indifference curves that “fan out” in the Marshack-Machina triangle, and thus can explain the well-known Allais and Common Ratio paradoxes that models such as prospect theory and regret theory are designed to capture. At the same time, our model is consistent with modern macroeconomic theory and evidence and generates predictions across a much wider set of domains than these models.

  • An Approximate Dual-Self Model and Paradoxes of Choice under
    2013
    Co-Authors: Drew Fudenberg, David K. Levine, Zacharias Maniadis
    Abstract:

    We derive a simplified version of the model of Fudenberg and Levine [2006, 2011] and show how this approximate model is useful in explaining choice under risk. We show that in the simple case of three outcomes, the model can generate indifference curves that “fan out ” in the Marshack-Machina triangle, and thus can explain the well-known Allais and Common Ratio paradoxes that models such as prospect theory and regret theory are designed to capture. At the same time, our model is consistent with modern macroeconomic theory and evidence and generates predictions across a much wider set of domains than these models

  • an approximate dual self model and paradoxes of choice under risk
    2012
    Co-Authors: Drew Fudenberg, David K. Levine, Zacharias Maniadis
    Abstract:

    We derive a simplified version of the model of Fudenberg and Levine, 2006 and Fudenberg and Levine, 2011 and show how this approximate model is useful in explaining choice under risk. We show that in the simple case of three outcomes, the model can generate indifference curves that “fan out†in the Marschak–Machina triangle, and thus can explain the well-known Allais and Common Ratio paradoxes that models such as prospect theory and regret theory are designed to capture. At the same time, our model is consistent with modern macroeconomic theory and evidence and generates predictions across a much wider set of domains than these models.