A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting

The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting. Exponential discounting has a well-established axiomatic foundation originally developed by Koopmans (Econometrica 28(2):287–309, 1960, 1972) and Koopmans et al. (Econometrica 32(1/2):82–100, 1964) with subsequent contributions by several other authors, including Bleichrodt et al. (J Math Psychol 52(6):341–347, 2008). The papers by Hayashi (J Econ Theory 112(2):343–352, 2003) and Olea and Strzalecki (Q J Econ 129(3):1449–1499, 2014) axiomatize quasi-hyperbolic discounting. The main contribution of this paper is to provide an alternative foundation for exponential and quasi-hyperbolic discounting, with simple, transparent axioms and relatively straightforward proofs. Using techniques by Fishburn (The foundations of expected utility. Reidel Publishing Co, Dordrecht, 1982) and Harvey (Manag Sci 32(9):1123–1139, 1986), we show that Anscombe and Aumann’s (Ann Math Stat 34(1):199–205, 1963) version of Subjective Expected Utility theory can be readily adapted to axiomatize the aforementioned types of discounting, in both finite and infinite horizon settings.     

All agreed: Aumann meets DeGroot

We represent consensus formation processes based on iterated opinion pooling (DeGroot in J Am Stat Assoc 69:118–121, 1974; Lehrer and Wagner in Rational consensus in science and society: a philosophical and mathematical study. Springer, Berlin, 1981) as a dynamic approach to common knowledge of posteriors (Aumann in Ann Stat 4(6):1236–1239, 1976; Geanakoplos and Polemarchakis in J Econ Theory 28:192–200, 1982). We thus provide a concrete and plausible Bayesian rationalization of consensus through iterated pooling. The link clarifies the conditions under which iterated pooling can be rationalized from a Bayesian perspective, and offers an understanding of iterated pooling in terms of higher-order beliefs.     

Optimal inequality behind the veil of ignorance

In Rawls’ (A theory of justice. Harvard University Press, Cambridge, 1971) influential social contract approach to distributive justice, the fair income distribution is the one that an individual would choose behind a veil of ignorance. Harsanyi (J Polit Econ 61:434–435, 1953, J Polit Econ 63:309–332, 1955, Am Polit Sci Rev 69:594–606, 1975) treated this situation as a decision under risk and arrived at utilitarianism using expected utility theory. This paper investigates the implications of applying cumulative prospect theory instead, which better describes behavior under risk. I find that the specific type of inequality in bottom-heavy right-skewed income distributions, which includes the log-normal income distribution, could be perceived as desirable. This optimal inequality result contrasts the implications of other social welfare criteria.     

Lottery- and survey-based risk attitudes linked through a multichoice elicitation task

We analyze the results from three different risk attitude elicitation methods. First, the broadly used test by Holt and Laury (2002), HL, second, the lottery-panel task by Sabater-Grande and Georgantzis (2002), SG, and third, responses to a survey question on self-assessment of general attitude towards risk (Dohmen et al. 2011). The first and the second task are implemented with real monetary incentives, while the third concerns all domains in life in general. Like in previous studies, the correlation of decisions across tasks is low and usually statistically non-significant. However, when we consider only subjects whose behavior across the panels of the SG task is compatible with constant relative risk aversion (CRRA), the correlation between HL and self-assessed risk attitude becomes significant. Furthermore, the correlation between HL and SG also increases for CRRA-compatible subjects, although it remains statistically non-significant.     

Ensemble prospectism

Incomplete preferences displaying ‘mildly sweetened’ structure are common, yet theoretically problematic. This paper examines the properties of the rankings induced by the set of all coherent completions of the mildly sweetened partial preference structure. Building on these properties, I propose an ensemble-based refinement of Hare’s (Analysis 70:237–247, 2010) prospectism criterion for rational choice when preferences are incomplete. Importantly, this ensemble-based refinement is immune to Peterson’s (Theory and Decision 78:451–456, 2015) weak money pump argument. Hence, ensemble prospectism ensures outcome rationality. Furthermore, by recognizing the structural isomorphism between mildly sweetened preference structures and Cover’s splitting rule in Blackwell’s Pick the Largest Number problem (Ann Math Stat 22:393–399, 1951), ensemble prospectism can be shown to yield better-than-even odds of selecting the ex-post higher utility option—despite the absence of all-things-considered preferences ex ante.     

Loss aversion leading to advantageous selection

Some insurance markets are characterized by “advantageous selection”, that is, ex-post risk and coverage are negatively correlated. We show that expectation-based loss aversion as in K?szegi and Rabin (Quarterly Journal of Economics, 121(4), 1133–1165, 2006; The American Economic Review, 97(4), 1047–1073, 2007) provides a natural explanation for this phenomenon in environments in which risk aversion models do not, e.g., when agents face modest-scale risks and/or in absence of moral hazard. More exposure to risk has two competing effects on an agent’s willingness to pay for insurance: a positive effect, as in standard expected utility models; and a negative one, due to a reference effect. We determine conditions under which an insurance provider optimally sets a high price at which only low risk agents buy.     

Strategic ambiguity and decision-making: an experimental study

We conducted a set of experiments to compare the effect of ambiguity in single-person decisions and games. Our results suggest that ambiguity has a bigger impact in games than in ball and urn problems. We find that ambiguity has the opposite effect in games of strategic substitutes and complements. This confirms a theoretical prediction made by Eichberger and Kelsey (J Econ Theory 106:436–466, 2002). In addition, we note that subjects’ ambiguity attitudes appear to be context dependent: ambiguity loving in single-person decisions and ambiguity averse in games. This is consistent with the findings of Kelsey and le Roux (Theory Decis 79:667–688, 2015).     

Conditional expected utility

Let \({\mathcal {E}}\) be a class of events. Conditionally Expected Utility decision makers are decision makers whose conditional preferences \(\succsim _{E}\), \(E\in {\mathcal {E}}\), satisfy the axioms of Subjective Expected Utility (SEU) theory. We extend the notion of unconditional preference that is conditionally EU to unconditional preferences that are not necessarily SEU. We study a subclass of these preferences, namely those that satisfy dynamic consistency. We give a representation theorem, and show that these preferences are Invariant Bi-separable in the sense of Ghirardato et al. (Journal of Economic Theory 118:133–173, 2004). We also show that these preferences have only a trivial overlap with the class of Choquet Expected Utility preferences, but there are plenty of preferences of the \(\alpha \)-Maxmin Expected Utility type that satisfy our assumptions. We identify several concrete settings where our results could be applied. Finally, we consider the special case where the unconditional preference is itself SEU, and compare our results with those of Fishburn (Econometrica 41:1–25, 1973).     

Asymmetric Choquet random walks and ambiguity aversion or seeking

Asymmetric Choquet random walks are defined, in the form of dynamically consistent random walks allowing for asymmetric conditional capacities. By revisiting Kast and Lapied (Dynamically consistent Choquet random walk and real investments. Document de Travail n. 2010-33, GREQAM, HAL id: halhs-00533826, 2010b) and Kast et al. (Econ Model, 38:495–503, 2014) we show that some findings regarding the effects of ambiguity aversion are preserved in the more general framework, which is of interest in several applications to policy making, risk management, corporate decisions, real option valuation of investment/ disinvestment projects, etc. The effect of ambiguity on the higher moments is investigated, as well, as they have an interpretation in terms of the psychological attitude of a decision-maker towards ambiguity. Finally, some financial applications are provided as an illustration.     

Risk preferences of Australian academics: where retirement funds are invested tells the story

Risk preferences of Australian academics are elicited by analyzing the aggregate distribution of their retirement funds (superannuation) across available investment options. Not more than 10 % of retirement funds are invested as if their owners maximize expected utility under the assumption of constant relative risk aversion with an empirically plausible level of risk aversion. An implausibly high level of risk aversion is required to rationalize any investment into bonds when stocks are available. Not more than 36.54 % of all investments can be rationalized by a model of loss averse preferences. Moreover, the levels of loss aversion typically reported in the experimental studies imply overinvestment in bonds, which is not observed in the data. Up to 67.18 % of all investments can be rationalized by rank-dependent utility or Yaari’s (Econometrica 55:95–115 1987) dual model with empirically plausible parameters. A median Australian academic behaves as if maximizing rank-dependent utility with parameter \(\gamma \in [0.76, 0.79]\) in a Tversky and Kahneman (J Risk Uncertain 5:297–323 1992) probability weighting function.     

A note on budget constraints and outside options in common agency

Bernheim and Whinston (Q J Econ 101:1–31, 1986) show that, in a common agency problem without budget constraints, the set of Nash equilibria with truthful strategies (TNE), the set of coalition-proof Nash equilibria (CPNE), and the principal-optimal core of the underlying coalitional game are non-empty and all equivalent in payoff space. We show that, with budget constraints, none of Bernheim and Whinston’s (Q J Econ 101:1–31, 1986) results hold: (i) a CPNE may not exist, (ii) a TNE may not exist even when a CPNE exists, (iii) a TNE may not be a CPNE, and (iv) both TNE and CPNE payoffs are core allocations but are not necessarily principal-optimal. However, when principals have outside options but no budget constraints, (i), and (iii) continue to hold but not for (ii) and (iv). In particular, a TNE always exists but the core may be empty.     

Piecewise linear rank-dependent utility

Choice under risk is modelled using a piecewise linear version of rank-dependent utility. This model can be considered a continuous version of NEO-expected utility (Chateauneuf et al., J Econ Theory 137:538–567, 2007). In a framework of objective probabilities, a preference foundation is given, without requiring a rich structure on the outcome set. The key axiom is called complementary additivity.     

Modelling curiosity in decision-making

This paper develops a model of choice with an agent that is capable of experiencing curiosity using Loewenstein’s (Psychol Bull 116(1):75–98, 1994) information gap interpretation of curiosity. We then proceed to determine the restrictions on choice behaviour implied by the model in two choice environments: no discovery—where the Decision-Maker does not have the opportunity to learn—and discovery—where she is afforded such an opportunity. These restrictions can be applied by an observer to determine if a Decision-Maker’s choices align with the model.     

A note on a recent paper by Dagsvik on IIA and random utilities

In a recent paper in this journal, Dagsvik derives the class of independent random utility representations that are “equivalent” to the independence-from-irrelevant-alternatives (IIA) assumption by Luce (Individual choice behavior: a theoretical analysis. Wiley, New York, 1959). In this short note, we clarify the relations between this paper by Dagsvik, and a paper in Lindberg’s 2012 thesis.     

Liberal–conservative self-identification in Korea: a cross-cultural explanation

Two sets of explanations for the liberal–conservative political orientation developed and tested in the U.S. were compared and tested with Korean data. The two sets of explanations are (1) Moral Foundations Theory that states that liberals and conservatives have different moral intuitions (Haidt and Graham, Soc Justice Res 20:98–116, 2007) and (2) a theory that cognitive needs to manage uncertainty and threat are the main factors behind the political orientation (Jost et al., Psychol Bull 129:339–375, 2003). These two sets of explanation for political orientation were tested and supported empirically in the U.S. The Korean data showed clear support for the Moral Foundations Theory. Compared to conservatives, liberals in South Korea agreed more with individual oriented moral statements and less with community oriented moral statements. The data showed weak support for the uncertainty and threat explanation in that conservatives showed higher level of intolerance to ambiguity and higher level of death anxiety, but the correlations are weak. Implications of these findings were discussed.     

When and how to satisfice: an experimental investigation

This paper is about satisficing behaviour. Rather tautologically, this is when decision-makers are satisfied with achieving some objective, rather than in obtaining the best outcome. The term was coined by Simon (Q J Econ 69:99–118, 1955), and has stimulated many discussions and theories. Prominent amongst these theories are models of incomplete preferences, models of behaviour under ambiguity, theories of rational inattention, and search theories. Most of these, however, seem to lack an answer to at least one of two key questions: when should the decision-maker (DM) satisfice; and how should the DM satisfice. In a sense, search models answer the latter question (in that the theory tells the DM when to stop searching), but not the former; moreover, usually the question as to whether any search at all is justified is left to a footnote. A recent paper by Manski (Theory Decis. doi: 10.1007/s11238-017-9592-1, 2017) fills the gaps in the literature and answers the questions: when and how to satisfice? He achieves this by setting the decision problem in an ambiguous situation (so that probabilities do not exist, and many preference functionals can therefore not be applied) and by using the Minimax Regret criterion as the preference functional. The results are simple and intuitive. This paper reports on an experimental test of his theory. The results show that some of his propositions (those relating to the ‘how’) appear to be empirically valid while others (those relating to the ‘when’) are less so.     

A Culturally Competent Family Enhancement and Empowerment Model for African American Parents

The National Association of Social Worker's Standards for Cultural Competence (2002 National Association of Social Workers. 2002. NASW standards for cultural competence in social work practice, Washington, DC: Author.  [Google Scholar]) mandates social work practices that recognize the cultural preferences of different groups in the United States. The NASW Code of Ethic (1996 National Association of Social Workers. 1996. Code of ethics, Washington, DC: NASW Press.  [Google Scholar]) states that social workers have a responsibility to understand culture and its function and to further recognize the strengths that exist in all cultures. This article addresses the void in the social work literature on culturally based and strengths‐oriented family interventions for African American parents. The article describes a culturally competent intervention model developed by the MAAT Center for Human and Organizational Enhancement, Inc. in Washington, D.C. for parents of African American male youths who live in high‐risk environments. The family enhancement and empowerment model (FEEM) is based on Africentric social work principles that are grounded in a strengths perspective. The article describes the FEEM program, including a discussion of practical strategies for building trust and offering support to African American parents and families.     

Subgame perfect equilibrium in a bargaining model with deterministic procedures

Two players, A and B, bargain to divide a perfectly divisible pie. In a bargaining model with constant discount factors, \(\delta _A\) and \(\delta _B\), we extend Rubinstein (Econometrica 50:97–110, 1982)’s alternating offers procedure to more general deterministic procedures, so that any player in any period can be the proposer. We show that each bargaining game with a deterministic procedure has a unique subgame perfect equilibrium (SPE) payoff outcome, which is efficient. Conversely, each efficient division of the pie can be supported as an SPE outcome by some procedure if \(\delta _A+\delta _B\ge 1\), while almost no division can ever be supported in SPE if \(\delta _A+\delta _B < 1\).     

Two simple characterizations of the Nash bargaining solution

We provide two alternative characterizations of the Nash bargaining solution. We introduce new simple axioms, strong undominatedness by the disagreement point, and egalitarian Pareto optimality. First, we prove that the Nash solution is characterized by symmetry, scale invariance, independence of irrelevant alternatives, and strong undominatedness by the disagreement point. Second, we replace the independence of irrelevant alternatives axiom with the sandwich axiom (Rachmilevitch in Theory Decis 80:427–442, 2016) and egalitarian Pareto optimality. We then demonstrate that the Nash solution is characterized by symmetry, scale invariance, strong undominatedness by the disagreement point, the sandwich axiom, and egalitarian Pareto optimality.     

The curse of hope

In K?szegi and Rabin’s (Q J Econ 1133–1165, 2006, Am Econ Rev 97:1047–1073, 2007) reference-dependent model of preferences, the chance of obtaining a better outcome can reduce an agent’s expected utility through an increase in the stochastic reference point. This means that individuals may prefer stochastically dominated lotteries. In this sense, hope, understood as a small probability of a better outcome, can be a curse. While K?szegi and Rabin focus on a linear specification of the utility function, we show that this effect occurs more broadly. Using fairly plausible assumptions and parameter values, we specify the conditions under which it occurs, as well as the type of lotteries in which this should be expected. We then show that while a simple subjective transformation of probability into weights of the reference point may in some cases mitigate the issue, in others, it can intensify it or even generate new ones. Finally, we extend the model by adding the individual’s current reference point (status quo) to the stochastic reference point. We show that this modification can reconcile K?szegi and Rabin’s model with the apparent empirical infrequency of stochastically dominated choices while maintaining its main qualitative results.