Peter P. Wakker

Max Planck Institute for Human Development, Berlín, Berlin, Germany

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Publications (150)163.23 Total impact

  • Amit Kothiyal, Vitalie Spinu, Peter P. Wakker
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    ABSTRACT: Prospect theory is the most popular theory for predicting decisions under risk. This paper investigates its predictive power for decisions under ambiguity, using its specification through the source method. We find that it outperforms its most popular alternatives, including subjective expected utility, Choquet expected utility, and three multiple priors theories: maxmin expected utility, maxmax expected utility, and a-maxmin expected utility.
    Journal of Risk and Uncertainty 02/2014; 48(1). · 1.53 Impact Factor
  • Amit Kothiyal, Vitalie Spinu, Peter P. Wakker
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    ABSTRACT: This paper provides necessary and sufficient preference conditions for average utility maximization over sequences of variable length. We obtain full generality by using a new algebraic technique that exploits the richness structure naturally provided by the variable length of the sequences. Thus we generalize many preceding results in the literature. For example, continuity in outcomes, a condition needed in other approaches, now is an option rather than a requirement. Applications to expected utility, decisions under ambiguity, welfare evaluations for variable population size, discounted utility, and quasilinear means in functional analysis are presented.
    Operations Research 02/2014; 62(1). · 1.79 Impact Factor
  • Chen Li, Zhihua Li, Peter P. Wakker
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    ABSTRACT: A central question in many debates on paternalism is whether a decision analyst can ever go against the stated preference of a client, even if merely intending to improve the decisions for the client. Using four gedanken-experiments, this paper shows that this central question, so cleverly and aptly avoided by libertarian paternalism (nudge), cannot always be avoided. The four thought experiments, while purely hypothetical, serve to raise and specify the critical arguments in a maximally clear and pure manner. The first purpose of the paper is, accordingly, to provide a litmus test on the readers’ stance on paternalism. We thus also survey and organize the various stances in the literature. The secondary purpose of this paper is to argue that paternalism cannot always be avoided and consumer sovereignty cannot always be respected. However, this argument will remain controversial.
    Theory and Decision 01/2014; · 0.48 Impact Factor
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    ABSTRACT: Doyle’s (2013) theoretical survey of discount functions criticizes two parametric families abbreviated as CRDI and CADI families. We show that Doyle’s criticisms are based on a mathematical mistake and are incorrect.
    Judgment and decision making 09/2013; 2013(8):630-631. · 2.62 Impact Factor
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    ABSTRACT: Behavioral conditions such as compound invariance for risky choice and constant decreasing relative impatience for intertemporal choice have surprising implications for the underlying decision model. They imply a multiplicative separability of outcomes and either probability or time. Hence the underlying model must be prospect theory or discounted utility on the domain of prospects with one nonzero outcome. We indicate implications for richer domains with multiple outcomes, and with both risk and time involved.
    Journal of Mathematical Psychology 06/2013; 57(s 3–4):68–77. · 1.62 Impact Factor
  • Vitalie Spinu, Peter P. Wakker
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    ABSTRACT: This paper presents preference axiomatizations of expected utility for nonsimple lotteries while avoiding continuity constraints. We use results by Fishburn (1975), Wakker (1993), and Kopylov (2010) to generalize results by Delbaen et al. (2011). We explain the logical relations between these contributions for risk versus uncertainty, and for finite versus countable additivity, indicating what are the most general axiomatizations of expected utility existing today.
    Journal of Mathematical Economics 01/2013; 49(1):28–30. · 0.32 Impact Factor
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    Peter P. Wakker
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    ABSTRACT: This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s classical result, AND can therefore be applied TO ANY finite Bayesian network.It neither requires linear utility AS did de Finetti s classical result, AND r ntherefore allows FOR the empirically AND normatively desirable risk r naversion.Finally, BY identifying AND fixing utility IN an elementary r nmanner, our result can readily be applied TO identify methods OF r nprobability updating.Thus, a decision - theoretic foundation IS given r nto the computationally efficient method OF inductive reasoning r ndeveloped BY Rudolf Carnap.Finally, recent empirical findings ON r nprobability assessments are discussed.It leads TO suggestions FOR r ncorrecting biases IN probability assessments, AND FOR an alternative r nto the Dempster - Shafer belief functions that avoids the reduction TO r ndegeneracy after multiple updatings.r n
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    Baillon, Bram Driesen, Peter P. Wakker
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    ABSTRACT: This paper presents a general technique for comparing the concavity of different utility functions when probabilities need not be known. It generalizes: (a) Yaariʼs comparisons of risk aversion by not requiring identical beliefs; (b) Kreps and Porteusʼ information-timing preference by not requiring known probabilities; (c) Klibanoff, Marinacci, and Mukerjiʼs smooth ambiguity aversion by not using subjective probabilities (which are not directly observable) and by not committing to (violations of) dynamic decision principles; (d) comparative smooth ambiguity aversion by not requiring identical second-order subjective probabilities. Our technique completely isolates the empirical meaning of utility. It thus sheds new light on the descriptive appropriateness of utility to model risk and ambiguity attitudes.
    Games and Economic Behavior 07/2012; 75(2):481–489. · 0.83 Impact Factor
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    Arthur E Attema, Han Bleichrodt, Peter P Wakker
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    ABSTRACT: Time discounting and quality of life are two important factors in evaluations of medical interventions. The measurement of these two factors is complicated because they interact. Existing methods either simply assume one factor given, based on heuristic assumptions, or invoke complicating extraneous factors, such as risk, that generate extra biases. The authors introduce a method for measuring discounting (and then quality of life) that involves no extraneous factors and that avoids distorting interactions. Their method is considerably simpler and more realistic for subjects than existing methods. It is entirely choice based and thus can be founded on economic rationality requirements. An experiment demonstrates the feasibility of this method and its advantages over classical methods.
    Medical Decision Making 06/2012; 32(4):583-93. · 2.89 Impact Factor
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    ABSTRACT: In a large representative sample, we measure ambiguity attitudes and investigate their relation with stock market participation. Our tractable measurement of the general population’s ambiguity attitudes is made possible by a simplification of the recently introduced source method. In addition to ambiguity aversion, the results from our representative sample confirm a-insensitivity, a new component of ambiguity attitudes recently found in laboratory studies. A-insensitivity means that people do not sufficiently discriminate between different levels of likelihood, often treating them as fifty-fifty. Contrary to common expectation, ambiguity aversion, when measured using classical stimuli, is not significantly associated with stock market participation, except for those subjects who perceive stock returns as highly ambiguous. A-insensitivity, however, is negatively related to both stock market participation and private business ownership. These surprising findings can be explained by reference dependent ambiguity. Our results show the empirical relevance of a-insensitivity and reference dependence for real-world economic decisions.
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    ABSTRACT: Two experiments show that violations of expected utility due to ambiguity, found in general decision experiments, also affect belief aggregation. Hence we use modern ambiguity theories to analyze belief aggregation, thus obtaining more refined and empirically more valid results than traditional theories can provide. We can now confirm more reliably that conflicting (heterogeneous) beliefs where some agents express certainty are processed differently than informationally equivalent imprecise homogeneous beliefs. We can also investigate new phenomena related to ambiguity. For instance, agents who express certainty receive extra weight (a cognitive effect related to ambiguity-generated insensitivity) and generate extra preference value (source preference; a motivational effect related to ambiguity aversion). Hence, incentive compatible belief elicitations that prevent manipulation are especially warranted when agents express certainty. For multiple prior theories of ambiguity, our findings imply that the same prior probabilities can be treated differently in different contexts, suggesting an interest of corresponding generalizations.
    Journal of Risk and Uncertainty 01/2012; 44(2):115-147. · 1.53 Impact Factor
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    ABSTRACT: This paper finds preference reversals in measurements of ambiguity aversion, even if psychological and informational circumstances are kept constant. The reversals are of a fundamentally different nature than the reversals found before because they cannot be explained by context-dependent weightings of attributes. We offer an explanation based on Sugden's random-reference theory, with different elicitation methods generating different random reference points. Then measurements of ambiguity aversion that use willingness to pay are confounded by loss aversion and hence overestimate ambiguity aversion. This paper was accepted by Teck Ho, decision analysis.
    Management Science 07/2011; 57:1320-1333. · 1.86 Impact Factor
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    Gijs van de Kuilen, Peter P. Wakker
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    ABSTRACT: This paper introduces a parameter-free method for measuring the weighting functions of prospect theory and rank-dependent utility. These weighting functions capture risk attitudes, subjective beliefs, and ambiguity attitudes. Our method, called the midweight method, is based on a convenient way to obtain midpoints in the weighting function scale. It can be used both for risk (known probabilities) and for uncertainty (unknown probabilities). The resulting integrated treatment of risk and uncertainty is particularly useful for measuring ambiguity, i.e., the difference between uncertainty and risk. Compared to existing methods to measure weighting functions and attitudes toward uncertainty and ambiguity, our method is more efficient and can accommodate violations of expected utility under risk. An experiment demonstrates the tractability of our method, yielding plausible results such as ambiguity aversion for moderate and high likelihoods but ambiguity seeking for low likelihoods, as predicted by Ellsberg. This paper was accepted by George Wu, decision analysis.
    Management Science 01/2011; 57:582-598. · 1.86 Impact Factor
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    Han Bleichrodt, Jason N, Martin Filko, Peter P. Wakker
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    ABSTRACT: Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the measurement of quality-adjusted life-years (QALY) in the health domain.
    Journal of Mathematical Psychology 01/2011; · 1.62 Impact Factor
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    Amit Kothiyal, Vitalie Spinu, Peter P. Wakker
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    ABSTRACT: Preference foundations give necessary and sufficient conditions for a decision model, stated directly in terms of the empirical primitive: the preference relation. For the most popular descriptive model for decision making under risk and uncertainty today, prospect theory, preference foundations have as yet been provided only for prospects taking finitely many values. In applications, however, prospects often are complex and involve infinitely many values, as in normal and lognormal distributions. This paper provides a preference foundation of prospect theory for such complex prospects. We allow for unbounded utility and only require finite additivity of the underlying probability distributions, leaving the restriction to countably additive distributions optional. As corollaries, we generalize previously obtained preference foundations for special cases of prospect theory (rank-dependent utility and Choquet expected utility) that all required countable additivity. We now obtain genuine generalizations of de Finetti’s and Savage’s finitely additive setups to unbounded utility. KeywordsProspect theory–Preference foundations–Continuous distributions–Unbounded utility
    Journal of Risk and Uncertainty 01/2011; 42(3):195-210. · 1.53 Impact Factor
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    Peter P. Wakker
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    ABSTRACT: This paper discusses Jean-Yves Jaffray’s ideas on ambiguity and the views underlying his ideas. His models, developed 20years ago, provide the most tractable separation of risk attitudes, ambiguity attitudes, and ambiguity beliefs available in the literature today. KeywordsAmbiguity–Total absence of information–Belief functions
    Theory and Decision 01/2011; 71(1):11-22. · 0.48 Impact Factor
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    Stefan T. Trautmann, Peter P. Wakker
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    ABSTRACT: When process fairness deviates from outcome fairness, dynamic inconsistencies can arise as in nonexpected utility. Resolute choice (Machina) can restore dynamic consistency under nonexpected utility without using Strotz's precommitment. It can similarly justify dynamically consistent process fairness.
    Economics Letters. 12/2010; 109(3):187-189.
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    Amit Kothiyal, Vitalie Spinu, Peter P. Wakker
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    ABSTRACT: Proper scoring rules serve to measure subjective degrees of belief. Traditional proper scoring rules are based on the assumption of expected value maximization. There are, however, many deviations from expected value, primarily due to risk aversion. Correcting techniques have been proposed in the literature for deviations due to nonlinear utility. These techniques still assumed expected utility maximization. More recently, corrections for deviations from expected utility have been proposed. The latter concerned, however, only the quadratic scoring rule, and could handle only half of the domain of subjective beliefs. Further, beliefs close to 0.5 could not be discriminated. This paper generalizes the correcting techniques to all bounded binary proper scoring rules, covers the whole domain of beliefs and, in particular, can discriminate between all degrees of belief. Thus, we fully extend the properness requirement (in the sense of identifying all degrees of subjective beliefs) to virtually all models that deviate from expected value. Copyright © 2011 John Wiley & Sons, Ltd.
    Journal of Multi-Criteria Decision Analysis 04/2010; 17(3‐4):101 - 113.
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    ABSTRACT: In economic decisions we often have to deal with uncertain events for which no probabilities are known. Several normative models have been proposed for such decisions. Empirical studies have usually been qualitative, or they estimated ambiguity aversion through one single number. This paper introduces the source method, a tractable method for quantitatively analyzing uncertainty empirically that can capture the richness of ambiguity attitudes. The theoretical key in our method is the distinction between different sources of uncertainty, within which subjective (choice-based) probabilities can still be defined. Source functions convert those subjective probabilities into willingness to bet. We apply our method in an experiment, where we do not commit to particular ambiguity attitudes but let the data speak.

Publication Stats

4k Citations
163.23 Total Impact Points


  • 2014
    • Max Planck Institute for Human Development
      Berlín, Berlin, Germany
  • 1994–2014
    • Erasmus Universiteit Rotterdam
      • Department of Economics
      Rotterdam, South Holland, Netherlands
  • 2009
    • Universidade Autónoma de Lisboa Luís de Camoes
      • Department of Psychology and Sociology
      Lisbon, Lisbon, Portugal
  • 2008
    • Université de Cergy-Pontoise
      95001 CEDEX, Ile-de-France, France
  • 2006
    • Los Andes University (Colombia)
      Μπογκοτά, Bogota D.C., Colombia
    • Kent State University
      • Department of Economics
      Kent, OH, United States
  • 2000–2006
    • University of Amsterdam
      • Department of Economics
      Amsterdamo, North Holland, Netherlands
  • 2004–2005
    • Maastricht University
      • Department of Quantitative Economics
      Maastricht, Provincie Limburg, Netherlands
  • 1970–2002
    • Tilburg University
      • CentER for Research in Economics and Business " CentER"
      Tilburg, North Brabant, Netherlands
  • 1970–2001
    • Leiden University Medical Centre
      • Department of Medical Decision Making
      Leiden, South Holland, Netherlands
  • 1993–1998
    • Leiden University
      Leyden, South Holland, Netherlands
  • 1990–1991
    • Duke University
      • Fuqua School of Business
      Durham, North Carolina, United States
  • 1985–1991
    • Radboud University Nijmegen
      • Department of Mathematics
      Nymegen, Gelderland, Netherlands
  • 1989
    • Centraal Bureau voor de Statistiek
      's-Gravenhage, South Holland, Netherlands