Subjective expected utility: A review of normative theories

This paper reviews theories of subjective expected utility for decision making under uncertainty. It focuses on normative interpretations and discusses the primitives, axioms and representation-uniqueness theorems for a number of theories. Similarities and differences among the various theories are highlighted. The interplay between realistic decision structures and structural axioms that facilitate mathematical derivations is also emphasized.The review attempts to be complete up to 1980. Among others, it includes theories developed by Ramsey; Savage; Suppes; Davidson and Suppes; Anscombe and Aumann; Pratt, Raiffa and Schlaifer; Fishburn; Bolker; Jeffrey; Pfanzagl; Luce and Krantz.     

Objective and subjective rationality and decisions with the best and worst case in mind

Theory and Decision - We study decision under uncertainty in an Anscombe–Aumann framework. Two binary relations characterize a decision-maker: one (in general) incomplete relation, reflecting...     

Expected discounted utility

Standard axioms of additively separable utility for choice over time and classic axioms of expected utility theory for choice under risk yield a generalized expected additively separable utility representation of risk-time preferences over probability distributions over sure streams of intertemporal outcomes. A dual approach is to use the analogues of the same axioms in a reversed order to obtain a generalized additively separable expected utility representation of time–risk preferences over intertemporal streams of probability distributions over sure outcomes. The paper proposes an additional axiom, which is called risk-time reversal, for obtaining a special case of the two representations—expected discounted utility. The axiom of risk-time reversal postulates that if a risky lottery over streams of sure intertemporal outcomes and an intertemporal stream of risky lotteries yield the same probability distribution of possible outcomes in every point in time then a decision-maker is indifferent between the two. This axiom is similar to assumption 2 “reversal of order in compound lotteries” in Anscombe and Aumann (Ann Math Stat 34(1):199–205, 1963, p. 201).

     

A simplified axiomatic approach to ambiguity aversion

This paper takes the Anscombe–Aumann framework with horse and roulette lotteries, and applies the Savage axioms to the horse lotteries and the von Neumann–Morgenstern axioms to the roulette lotteries. The resulting representation of preferences yields a subjective probability measure over states and two utility functions, one governing risk attitudes and one governing ambiguity attitudes. The model is able to accommodate the Ellsberg paradox and preferences for reductions in ambiguity.     

Ambiguity framed

In his exposition of subjective expected utility theory, Savage (1954) proposed that the Allais paradox could be reduced if it were recast into a format which made the appeal of the independence axiom of expected utility theory more transparent. Recent studies consistently find support for this prediction. We consider a salience-based choice model which explains this frame-dependence of the Allais paradox. We then derive the novel prediction that the presentation format responsible for reductions in Allais-style violations of expected utility theory will also reduce Ellsberg-style violations of subjective expected utility theory. This format makes the appeal of Savage’s “sure thing principle” more transparent. We design an experiment to test this prediction and find strong support for such frame-dependence of ambiguity aversion in Ellsberg-style choices. In particular, we observe markedly less ambiguity-averse behavior in Savage’s matrix format than in a more standard “prospect” format. This finding poses a new challenge for the leading models of ambiguity aversion.     

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.     

Subjective beliefs and confidence when facts are forgotten

Forgetting can be a salient source of uncertainty for subjective beliefs, confidence, and ambiguity attitudes. To investigate this, we run several experiments where people bet on propositions (facts) that they cannot recall with certainty. We use betting preferences to infer subjects’ revealed beliefs and their revealed confidence in these beliefs. Forgetting is induced via interference tasks and time delays (up to one year). We observe a natural memory decay pattern where beliefs become less accurate and confidence is reduced as well. Moreover, we find a form of comparative ignorance where subjects are more ambiguity averse when they cannot recall the truth rather than never having learnt it. In a different vein, we identify an overconfidence pattern: on average, subjects overpay for bets on propositions that they believe in, but underpay for the opposite bets. We formulate a two-signal behavioral model of forgetting that generates all of these patterns. It suggests new testable hypotheses that are confirmed by our data.

     

Competence and consent to research: A critique of the recommendations of the national bioethics advisory commission*

Concern about the participation of incompetent subjects in psychiatric research has grown in the last several years. In response, the National Bioethics Advisory Commission (NBAC) recommended in its recent report that all investigations involving persons with mental disorders that may be associated with cognitive impairment that may pose greater than minimal risk to subjects utilize independent assessors to verify the capacities of subjects prior to entry into the study. This recommendation poses several problems for the conduct of research and the protection of research subjects. First, it fails to target that group of subjects most likely to be at risk for incapacity. Second, it focuses on too broad a range of research projects, many of which pose little risk to participants. The substantial costs of this approach are therefore not likely to be outweighed by concomitant benefits. In place of the NBAC recommendation, the author proposes a more flexible system of capacity assessment, designed to balance the costs with a greater likelihood of achieving meaningful protection for research subjects with mental disorders.     

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.     

A new test of convexity–concavity of discount function

Discounted utility theory and its generalizations (e.g., quasihyperbolic discounting, generalized hyperbolic discounting) use discount functions for weighting utilities of outcomes received in different time periods. We propose a new simple test of convexity–concavity of discount function. This test can be used with any utility function (which can be linear or not) and any preferences over risky lotteries (expected utility theory or not). The data from a controlled laboratory experiment show that about one third of experimental subjects reveal a concave discount function and another one third of subjects reveal a convex discount function (for delays up to two month).

     

Fear of Ruin

This paper offers interpretations and applications of the “fear of ruin” coefficient (Aumann and Kurz, 1977, Econometrica). This coefficient is useful for analyzing the behavior of expected utility maximizers when they face binary lotteries with the same worse outcome. Comparative statics results of “more fear of ruin” are derived. The partial ordering induced by the fear of ruin coefficient is shown to be weaker than that induced by the Arrow-Pratt coefficient. JEL Classification: D81     

Disappointment Aversion in internet Bidding-Decisions

The article presents an Internet experiment where subjects sequentially bid for basic gifts and binary-lotteries on these gifts in incentive compatible Vickrey auctions. Subjects exhibit uniformly pessimistic prize-weighting in spite of precautions to reduce suspicion and prohibit collusion. The bids for lotteries are close to the minimal payable value, even when the probability of obtaining a better prize is larger than 50%. Prize-weighting becomes even more conservative as the distance in value of payable prizes increases. The twofold aversive affect appears for three distinct groups of students; we demonstrate, however, that the same subjects overweight small win-probabilities in standard binary-choice.

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On matrix probabilities in nonarchimedean decision theory

In an earlier paper, we axiomatized a lexicographic expected utility model for preference in decision under uncertainty that is patterned on the models of Ramsey and Savage but omits their Archimedean axioms. Our model has the unusual feature that subjective probabilities are matrices that premultiply utility vectors in the lexicographic representation of preference between acts. Our purpose here is to analyze the model in relation to the Ramsey-Savage theory along with other models that have a lexicographic feature. A point of departure is Savage's postulate P4, whose purpose is to weakly order hisis more probable than relation on events. This postulate does not hold in our model and we therefore encounter incomparability between events. The paper explores the nature of incomparability, which can be widespread in high-dimensional situations. We include special cases of our model that retain a lexicographic component but also satisfy P4.     

Either with us or against us: experimental evidence on partial cartels

This paper analyzes the coordination challenge a partial cartel faces when payoff asymmetries between potential cartel insiders and potential cartel outsiders are large. We introduce two experimental treatments: a standard treatment where a complete cartel can be supported in a Nash equilibrium and a modified treatment where a complete cartel and a partial cartel can both be supported in a Nash equilibrium. To assess the role of communication both treatments are additionally run with a “chat option,” yielding four treatments in total. Our results show that subjects frequently reject the formation of partial cartels in the modified treatments. In all treatments with communication subjects are more likely to form complete cartels than partial cartels. The implications of these results are important for antitrust: payoff asymmetries between cartel members and outsiders may jeopardize the formation of partial cartels. Yet complete cartels may be formed instead, if institutional mechanisms with frequent communication are used to form cartels.

     

Resolving Beecher's Paradox: Getting beyond IRB reform

Protection of persons participating as research subjects is an essential element of ethical research conduct. There is growing concern that the existing system of institutional review boards (IRBs) and informed consent may not be adequate and is in need of reform. When science and medicine are “merged”; in clinical research, confusion of roles and conflicts of interests arise in relationships between patient‐subjects and physician‐investigators. IRBs have always had a primary role in protection of research participants. Their efforts to protect research subjects may make it more difficult for investigators to conduct research. This tension has lead to the development of an adversarial relationship between IRBs and investigators. Investigators and IRBs are also subject to external pressures that could impact efforts to protect research subjects. Efforts are underway to address these concerns. IRB reform, while needed, is not likely to be sufficient. Adoption of a new paradigm in which IRBs, investigators and research sponsors collectively accept protection of research subjects as their primary and shared responsibility may provide a more effective and efficient model that will be better able to deal with difficult ethical and social issues in clinical research.     

Frame modifications with a dying client

Abstract

This paper explores the nature of the treatment frame with a client in extreme circumstances. A move is made, through frame alterations, from a more “pure” technical mode to a more humanistic one. The costs and gains of these frame modifications are evaluated and the therapist's internal experience of the process presented. The paper concludes that the traditional frame is inadequate in therapy with a dying client. Blending the customary frame with a more flexible one more fully meets the needs of the client who is in extremis, enhancing treatment and the treatment alliance.     

Workplace Flexibility as an Organizational Response to the Aging of the Workforce: A Comparison of Nonprofit and For-Profit Organizations

ABSTRACT

The degree to which flexible work options are available to employees has been used as an indicator of the extent to which organizations have responded to workforce needs, including those related to the aging of the workforce. This article uses an organizational adaptation framework to determine factors that explain variation in the degree to which flexible work options are offered in for-profit and non-profit organizations. Findings indicate that while the scope of flexible work options offered was similar among for-profits and non-profits, the factors that predicted variance in the scope of these options differed somewhat between the two sectors.     

Minimax,information and ultrapessimism

Discussing the foundations of the minimax principle, Savage (1954) argued that it is utterly untenable for statistics because it is ultrapessimistic when applied to negative income, but claimed that such objection is not relevant when the principle is applied to regret. In this paper I rebut the latter claim. I first present an example where ultrapessimism, as Savage understood it, applies to minimax regret but not to minimax negative income. Then, for a sequential decision problems with two terminal acts and a finite number of states of nature, I give necessary and sufficient conditions for a decision rule to be ultrapessimistic, and show that for every payoff table with at least three states, be it in regret form or not, there exist an experiment such that the minimax rule is ultrapessimistic. I conclude with some more general remarks on information and the value of experimentation for a minimax agent.     

Management of quality assurance in clinical trials

Good Clinical Practices (GCP) were first established by the FDA and are now actively implemented by different countries. This becomes necessary as multinational large clinical programs are more complex, involving a large diversity of personnel and locations, with different practices of medicine and local regulatory requirements.

The responsibility of an independent Quality Assurance (QA) organization is to oversee the quality and integrity of research activities, and to assure compliance with company's regulatory requirements, and ethical considerations in order to facilitate worldwide registration of new compounds. The goal of a Clinical QA group is to provide continuous assistance to monitoring teams and investigators to ascertain authentic and reliable clinical trials. The Clinical QA programs must be flexible, calling for active communication and good understanding of quality requirements.

Clinical auditing is one of the instruments of Clinical QA. Study audit activities begin with the protocol, encompass all facets of the clinical trial and end with the final study report.

The focus of the presentation is geared towards auditing activities at investigator's site, purpose of which is to ensure that data gathered in the final clinical study report reflects the raw data collected at the source.     

Support in the Workplace: Buffering the Deleterious Effects of Work–Family Conflict on Child Welfare Workers’ Well-Being and Job Burnout

ABSTRACT

We examined the impact of work–family conflict (WFC) on worker well-being and job burnout, as well as the role of social support in the workplace as a potential buffer against the influence of WFC. Results of hierarchical multiple regression analyses in a cross-sectional sample of 361 public child welfare workers indicate that WFC was related to reduced well-being and increased job burnout, whereas supervisory support moderated the relationship between WFC and well-being. Findings from this study hold implications to workforce management practices aimed at improving worker well-being in human service and child welfare organizations. Human resource management policies designed to manage worker schedules should aim to facilitate workers’ ability to meet work and family demands through programs such as flexible work schedules and telecommuting. Recommendations for future research on WFC and worker well-being are discussed.