This paper aims to address the question of how one ought to choose when one is uncertain about what outcomes will result from one’s choices, but when one can nevertheless assign probabilities to the different possible outcomes. These choices are commonly referred to as choices (or decisions) under risk. I assume in this paper that one ought to make instrumentally rational choices—more precisely, one ought to adopt suitable means to one’s morally permissible ends. Expected utility (EU) theory is generally accepted (...) as a normative theory of rational choice under risk, or, more specifically, as a theory of instrumental rationality. According to EU theory, when faced with a decision under risk, one ought to rank one’s options (from least to most choiceworthy) according to their EU and one ought to choose whichever option carries the greatest EU (or one of them in the event that several alternatives are tied). The EU of an option is a probability-weighted sum of each of its possible utilities. In this paper, I argue that EU theory is not the correct theory of instrumental rationality. In its place, I argue for a new theory of instrumental rationality, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility of a in G—that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this principle, I then argue, roughly speaking, that for any agent, S, faced with any decision under risk, S ought to rank her options (in terms of how choiceworthy they are) according to their ECU and S ought to choose whichever option carries the greatest ECU (or one of them in the event that several alternatives are tied). For any option, a, a’s ECU is a probability‐weighted sum of a’s comparative utilities across the various possible states of the world. In this paper, I show that in some commonplace decisions under risk, ECU theory delivers different verdicts from those of EU theory. (shrink)

In this paper, I argue for a new normative theory of rational choice under risk, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility (CU) of a in G—that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this (...) principle, I then argue that for any agent, S, faced with any decision under risk, S should rank his or her decision options (in terms of how choiceworthy they are) according to their comparative expected comparative utility (CECU) and should choose whichever option carries the greatest CECU. For any option, a, a’s CECU is the difference between its ECU and that of whichever alternative to a carries the greatest ECU, where a’s ECU is a probability‐weighted sum of a’s CUs across the various possible states of the world. I lastly demonstrate that in some ordinary decisions under risk, ECU theory delivers different verdicts from those of standard decision theory. (shrink)

The goal of this article is to show that instrumental rationality and utility that have been used in economics for many years does not work well. What is presented in the article is how significant the influence of utilitarianism has been on economics and why the economists get rid of humans’ goals and motivations. It is shown in the article that the human who decides in present is absolutely different from the human who decides over time. Many economists neglected this (...) problem because they wanted to have an effective and simple model. Becker’s economic method is presented as a dead end to which economics has been brought to. It is impossible to connect different selves of one human being by using the utility measure. The works of Schelling and J.S. Mill are used to explain this impossibility. The conclusion of this article is that instrumental rationality and utility have affected economics significantly. But, this simplified view on human nature is no longer valid. Hence, economics needs to think not only about the means but also about the human goals. Economics needs to rebuff relativism and show people how to achieve well-being. If we want to help people with their self-governance, we will have to choose reason over emotions. (shrink)

In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a strategy (...) that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested. (shrink)

We develop a model of Disappointment in which disappointment and elation arise from comparing the outcome received, not with an expected value as in previous models, but rather with the other individual outcomes of the lottery. This approach may better reflect the way individuals are liable to experience disappointment. The model obtained accounts for classic behavioral deviations from the normative theory, offers a richer structure than previous disappointment models, and leads to a Rank-Dependent Utility formulation in a transparent way. Thus, (...) our disappointment model may provide a clear psychological rationale for the subjective transformation of probabilities. (shrink)

The literature contains evidence from some studies of asymmetric patterns of choice cycles in the direction consistent with regret theory, and evidence from other studies of asymmetries in the opposite direction. This article reports an experiment showing that both patterns occur within the same sample of respondents operating in the same experimental environment. We discuss the implications for modelling behaviour in such environments.

In the 1940s and 1950s thousands of lobotomies were performed on people with mental disorders. These operations were known to be dangerous, but thought to offer great hope. Nowadays, the lobotomies of the 1940s and 1950s are widely condemned. The consensus is that the practitioners who employed them were, at best, misguided enthusiasts, or, at worst, evil. In this paper I employ standard decision theory to understand and assess shifts in the evaluation of lobotomy. Textbooks of medical decision making generally (...) recommend that decisions under risk are made so as to maximise expected utility (MEU) I show that using this procedure suggests that the 1940s and 1950s practice of psychosurgery was justifiable. In making sense of this finding we have a choice: Either we can accept that psychosurgery was justified, in which case condemnation of the lobotomists is misplaced. Or, we can conclude that the use of formal decision procedures, such as MEU, is problematic. (shrink)

This research examines the moderating role of regret aversion in reason-based choice. Earlier research has shown that regret aversion and reason-based choice effects are linked through a common emphasis on decision justification, and that a simple manipulation of regret salience can eliminate the decoy effect, a well-known reason-based choice effect. We show here that the effect of regret salience varies in theory-relevant ways from one reason-based choice effect to another. For effects such as the select/reject and decoy effect, both of (...) which were independently judged to be unreasonable bases for deciding, regret salience eliminated the effect. For the most-important attribute effect that is judged to be normatively acceptable, however, regret salience amplified the effect. Anticipated self-blame regret and perceived decision justifiability consistently predicted preferences and thus offer a parsimonious account of both attenuation and amplification of these reason-based choice effects. (shrink)

Our aim in this paper was to establish an empirical evaluation for similarity effects modeled by Rubinstein; Azipurua et al.; Leland; and Sileo. These tests are conducted through a sensitivity analysis of two well-known examples of expected utility (EU) independence violations. We found that subjective similarity reported by respondents was explained very well by objective measures suggested in the similarity literature. The empirical results of this analysis also show that: (1) the likelihood of selection for the riskier choice increases as (...) the pair becomes more similar, (2) these choice patterns are consistent with well-known independence violations of expected utility, and (3) a significant proportion of individuals exhibit intransitive choice patterns predicted under similarity effects, but not allowed under generalized expected utility models for risky choice. (shrink)

Distortions in memory impose important bounds on rationality but have been largely disregarded in economics. While it is possible to learn, it is more difficult, and sometimes impossible, to unlearn. This retention effect lowers individual utility directly or via reduced productivity, and adds costs to principal-agent relationships. The engraving effect states that the more one tries to forget a piece of information the more vivid it stays in memory, leading to a paradoxical outcome. The effects are based on, and are (...) supported by, psychological experiments, and it is shown that they are relevant in many economic situations and beyond. (shrink)

Gupta has proposed a definition of strategic rationality cast in the framework of his revision theory of truth. His analysis, relative to a class of normal form games in which all players have a strict best reply to all other players’ strategy profiles, shows that game-theoretic concepts have revision-theoretic counterparts. We extend Gupta’s approach to deal with normal form games in which players’ may have weak best replies. We do so by adapting intuitions relative to Nash equilibrium refinements to the (...) revision-theoretic framework. We prove that there is a precise equivalence between trembling-hand perfect equilibria in two-player normal games and a revision-theoretic property. We then introduce lexicographic choice of action as a way to represent players’ expectations, which allows our analysis to reach full generality. Finally, we provide an example of the versatility of revision theory as applied to strategic interaction by formalizing a risk-and-compensation procedure of strategic choice in the revision-theoretic framework. (shrink)

Modeling risk in a prescriptively plausible way represents a major issue in decision theory. The benchmarking procedure, being based on the satisficing principle and providing a probabilistic interpretation of expected utility (EU) theory, is prescriptive. Because it is a target-based language, the benchmarking procedure can be applied naturally to finance. In finance, the centrality of risk is widely recognized, but the risk measures that are commonly used to assess risk are too poor as a decision making tool. In this paper (...) we propose a two-stage decision criterion of choice under risk that provides an application of benchmarking to finance through a risk measure. We will analyze some nonexpected utility theories, in particular lottery dependent utility, as potential frameworks for our criterion. (shrink)

Customers are increasingly talking positively about brands that are socially responsible and authentic. However, little empirical research has related corporate social responsibility (CSR) to brand authenticity and brand authenticity to customers’ positive word-of-mouth. Moreover, although highly attractive alternative brands are increasingly appearing in the marketplace, there is a lack of research examining the role of alternative attractiveness in the relationship between CSR and brand authenticity. We address these shortcomings in the literature drawing on data from 1,101 customers of insurance services (...) brands and analyze them using structural equation modeling. The findings show that CSR is positively related to customers’ positive word-of-mouth, both directly and indirectly, through brand authenticity. Moreover, alternative attractiveness positively moderates the effect of CSR on brand authenticity. This implies that CSR can act as a differentiation mechanism to further enhance the focal brand’s authenticity, when an alternative brand is perceived as highly attractive. (shrink)

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms or (...) conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity. To give the strategy more structure, philosophers have developed “principles of individuation”; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion. We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory. (shrink)

In the recent literature on episodic memory, there has been increasing recognition of the need to provide an account of its adaptive function. In this context, it is sometimes argued that episodic memory is critical for certain forms of decision making about the future. We criticize existing accounts that try to give episodic memory a role in decision making, before giving a novel such account of our own. This turns on the thought of a link between episodic memory and the (...) emotion of regret. We discuss how both experienced and anticipated regret can have a distinctive influence on decision making, and argue that the ability to recollect past events in episodic memory underpins the capacity to engage in the sophisticated types of mental time travel recruited in experiencing and anticipating regret. (shrink)

Incorporation of the behavioral issues of the decision maker (DM) is among the aspects that each Multicriteria Decision Making (MCDM) method implicitly or explicitly takes into account. As postulated by regret theory, the feelings of regret and rejoice are among the behavioral issues associated with the entire decision making process. Within the context of MCDM, the DM may feel regret, when the chosen alternative is compared with another one having at least one better criterion value. PROMETHEE II is a widely (...) known MCDM method that makes no explicit incorporation of regret attitude of the DM. In this paper, we elaborate on the applicability of regret theory to MCDM context. In particular, we investigate the findings of regret theory and explore the parallel between regret theory and PROMETHEE II method. Relying on the concepts of regret theory, we demonstrate how a decision that is made using a PROMETHEE II based outranking method conforms to the regret attitude of the DM. (shrink)

Regret and disappointment have in common the fact that they are experienced when the outcome of a decision is unfavourable: They both concern “what might have been”, had things been different. However, some regret and disappointment theorists regard the differences between these emotions as important, arguing that they differ with respect to the conditions under which they are felt, and how they affect decision making. The goal of the present research was to examine whether and how these emotions also differ (...) with respect to the way in which they are experienced. Participants were asked torecall aninstance of intense regret or disappointment andto indicate what they felt, thought, felt like doing, did, and were motivated to do during this experience (cf. Roseman, Wiest, & Swartz, 1994). Significant differences between regret and disappointment were found in every category. These differences were most pronounced for “action tendencies” (what participants felt like doing) and “emotivations” (what they were motivated to do). These results suggest that the two emotions have differential implications for future behaviour. (shrink)

In many real-world gambles, a non-trivial amount of time passes before the uncertainty is resolved but after a choice is made. An individual may have a preference between gambles with identical probability distributions over final outcomes if they differ in the timing of resolution of uncertainty. In this domain, utility consists not only of the consumption of outcomes, but also the psychological utility induced by an unresolved gamble. We term this utility anxiety. Since a reflective decision maker may want to (...) include anxiety explicitly in analysis of unresolved lotteries, a multiple-outcome model for evaluating lotteries with delayed resolution of uncertainty is developed. The result is a rank-dependent utility representation (e.g., Quiggin, 1982), in which period weighting functions are related iteratively. Substitution rules are proposed for evaluating compound temporal lotteries. The representation is appealing for a number of reasons. First, probability weights can be interpreted as the cognitive attention allocated to certain outcomes. Second, the model disaggregates strength of preference from temporal risk aversion and thus provides some insight into the old debate about the relationship between von Neumann–Morgenstern utility functions and strength of preference value functions. (shrink)

The rule to maximize expected utility is intended for decisions where options involve risk. In those decisions the decision maker's attitude toward risk is important, and the rule ought to take it into account. Allais's and Ellsberg's paradoxes, however, suggest that the rule ignores attitudes toward risk. This suggestion is supported by recent psychological studies of decisions. These studies present a great variety of cases where apparently rational people violate the rule because of aversion or attraction to risk. Here I (...) attempt to resolve the issue concerning expected utility and risk. I distinguish two versions of the rule to maximize expected utility. One adopts a broad interpretation of the consequences of an option and has great intuitive appeal. The other adopts a narrow interpretation of the consequences of an option and seems to have certain technical and practical advantages. I contend that the version of the rule that interprets consequences narrowly does indeed neglect attitudes toward risk. That version of the rule excludes the risk involved in an option from the consequences of the option and, contrary to what is usually claimed, cannot make up for this exclusion through adjustments in probability and utility assignments. I construct a new, general argument that establishes this in a rigorous way. On the other hand, I contend that the version of the rule that interprets consequences broadly takes account of attitudes toward risk by counting the risk involved in an option among the consequences of the option. I rebut some objections to this version of the rules, in particular, the objection that the rule lacks practical interest. Drawing upon the literature on 'mean-risk' decision rules, I show that this version of the rule can be used to solve some realistic decision problems. (shrink)

It is natural for humans to judge the outcome of a decision under uncertainty as a percentage of an ex-post optimal performance. We propose a robust decision-making framework based on a relative performance index. It is shown that if the decision maker’s preferences satisfy quasisupermodularity, single-crossing, and a nondecreasing log-differences property, the worst-case relative performance index can be represented as the lower envelope of two extremal performance ratios. The latter is used to characterize the agent’s optimal robust decision, which has (...) implications both computationally and for obtaining closed-form solutions. We illustrate our results in an application which compares the performance of relative robustness to solutions that optimize worst-case payoffs, maximum absolute regret, and expected payoffs under a Laplacian prior. (shrink)

A decision under ‘complete uncertainty’ is one where the decision maker knows the set of possible outcomes for each decision, but cannot assign probabilities to those outcomes. This way, the problem of ranking decisions is reduced to a problem of ranking sets of outcomes. All rankings that have emerged in the literature in this domain imply transitivity. In the current study, transitivity is subjected to an empirical evaluation in two experiments, where subjects are asked to choose between sets of monetary (...) consequences. After analysis with a Bayes Factor, very few violations of transitivity were found. It can be concluded that transitivity seems a plausible condition for the ranking of sets of monetary consequences. (shrink)

It is a familiar argument that advocates accommodating the so-called paradoxes of decision theory by abandoning the “independence” postulate. After all, if we grant that choice reveals preference, the anomalous choice patterns of the Allais and Ellsberg problems violate postulate P2 of Savage's system. The strategy of making room for new preference patterns by relaxing independence is adopted in each of the following works: Samuelson, Kahneman and Tversky's “Prospect Theory”, Allais and Hagen, Fishburn, Chew and MacCrimmon, McClennen, and in closely (...) argued essays by Machina. (shrink)

The devices with which experimental economists account for and justify their own and their opponents’ views are investigated by examining transcripts of interviews with two participants in experimental economics. The earlier investigations of natural scientists’ discourse provide material for comparisons. The results suggest that in assessing an opponent’s deviating view experimentalists in economics can be more cautious than natural scientists to characterize their opponents as influenced by personal and social factors. Indeed, they seem to admit that to some extent both (...) their own and their opponents’ behavior involves these influences. Regarding the development of disputes, the respondents constructed accounts where general optimism concerning the ability of empirical arguments to resolve disputes was linked with an idea of dialogues between theorists and experimentalists as vehicles of progress. (shrink)

(2013). Why humans are (sometimes) less rational than other animals: Cognitive complexity and the axioms of rational choice. Thinking & Reasoning: Vol. 19, No. 1, pp. 1-26. doi: 10.1080/13546783.2012.713178.

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. (shrink)

An unprocessed risk is a collection of simple lotteries with a reduction-rule that describes the actual-payoff to the decision-maker as a function of realized lottery outcomes. Experiments reveal that the willingness to pay for unprocessed risks is consistently biased toward the payoff-level in the unprocessed representation. The anchoring-to-frame bias in cases of positive framing is significantly weaker than in cases of negative framing suggesting that rational negativity bias may reflect in asymmetric violations of rationality.

By the late 1990s, several converging trends in economics, psychology, and neuroscience had set the stage for the birth of a new scientific field known as “neuroeconomics”. Without the availability of an extensive variety of experimental designs for dealing with individual and social decision-making provided by experimental economics and psychology, many neuroeconomics studies could not have been developed. At the same time, without the significant progress made in neuroscience for grasping and understanding brain functioning, neuroeconomics would have never seen the (...) light of day. The paper is an overview of the main significant advances in the knowledge of brain functioning by neuroscience that have contributed to the emergence of neuroeconomics and its rise over the past two decades. These advances are grouped over three non-independent topics referred to as the “emo-rational” brain, “social” brain, and “computational” brain. For each topic, it emphasizes findings considered as critical to the birth and development of neuroeconomics while highlighting some of prominent questions about which knowledge should be improved by future research. In parallel, it shows that the boundaries between neuroeconomics and several recent sub-fields of cognitive neuroscience, such as affective, social, and more generally, decision neuroscience, are rather porous. (shrink)

People often face preferential decisions under risk. To further our understanding of the cognitive processes underlying these preferential choices, two prominent cognitive models, decision field theory (DFT; Busemeyer & Townsend, 1993) and the proportional difference model (PD; González‐Vallejo, 2002), were rigorously tested against each other. In two consecutive experiments, the participants repeatedly had to choose between monetary gambles. The first experiment provided the reference to estimate the models’ free parameters. From these estimations, new gamble pairs were generated for the second (...) experiment such that the two models made maximally divergent predictions. In the first experiment, both models explained the data equally well. However, in the second generalization experiment, the participants’ choices were much closer to the predictions of DFT. The results indicate that the stochastic process assumed by DFT, in which evidence in favor of or against each option accumulates over time, described people’s choice behavior better than the trade‐offs between proportional differences assumed by PD. (shrink)

In this paper we experimentally investigate the disparity between willingness-to-accept (WTA) and willingness-to-pay (WTP) for risky lotteries. The direction of the income effect is reversed by endowing subjects with the highest price of a lottery when asking the WTP question. Our results show that the income effect is too small to be the only source of the disparity. Since the disparity concentrates on a subsample of subjects, parametric and nonparametric tests of the WTA-WTP ratio may lead to contradictory results. The (...) disparity is significantly reduced when background risk is introduced. That is, putting subjects always into a risky position could improve the contingent valuation method, which is often concerned with the assessment of risky situations such as health risks, automobile safety, etc. (shrink)

In most forms of evaluation the benefits of preventive health care are narrowly defined in terms of reductions in future morbidity and mortality. Thus it is normally assumed that it is the final health gains alone which bear utility. This discounts the possibility that individuals may derive utility from the process of health care and other outcomes as well as the end health states. Attributes such as anxiety, reassurance, autonomy, regret and hope provide potential benefits or disbenefits in addition to (...) health gains. This paper explores the concept of process utility in the specific context of preventive goods. Characteristics such as information, awareness and autonomy are examined for two preventive goods—hip protectors and mammographic screening. If individuals trade off process attributes for final health outcomes, then to ignore process utility may lead to a sub-optimal allocation of resources. (shrink)

The understanding of decision-making systems has come together in recent years to form a unified theory of decision-making in the mammalian brain as arising from multiple, interacting systems (a planning system, a habit system, and a situation-recognition system). This unified decision-making system has multiple potential access points through which it can be driven to make maladaptive choices, particularly choices that entail seeking of certain drugs or behaviors. We identify 10 key vulnerabilities in the system: (1) moving away from homeostasis, (2) (...) changing allostatic set points, (3) euphorigenic signals, (4) overvaluation in the planning system, (5) incorrect search of situation-action-outcome relationships, (6) misclassification of situations, (7) overvaluation in the habit system, (8) a mismatch in the balance of the two decision systems, (9) over-fast discounting processes, and (10) changed learning rates. These vulnerabilities provide a taxonomy of potential problems with decision-making systems. Although each vulnerability can drive an agent to return to the addictive choice, each vulnerability also implies a characteristic symptomology. Different drugs, different behaviors, and different individuals are likely to access different vulnerabilities. This has implications for an individual's susceptibility to addiction and the transition to addiction, for the potential for relapse, and for the potential for treatment. (shrink)

In our target article, we proposed that addiction could be envisioned as misperformance of a decision-making machinery described by two systems (deliberative and habit systems). Several commentators have argued that Pavlovian learning also produces actions. We agree and note that Pavlovian action-selection will provide several additional vulnerabilities. Several commentators have suggested that addiction arises from sociological parameters. We note in our response how sociological effects can change decision-making variables to provide additional vulnerabilities. Commentators generally have agreed that our theory provides (...) a framework within which to site addiction and treatment, but additional work will be needed to determine whether our taxonomy will help identify and treat subpopulations within the addicted community. (shrink)

Three experiments investigated the contrasting predictions of the evolutionary and decision-theoretic approaches to deontic reasoning. Two experiments embedded a hazard management (HM) rule in a social contract scenario that should lead to competition between innate modules. A 3rd experiment used a pure HM task. Threatening material was also introduced into the antecedent, p, of a deontic rule, if p then must q. According to the evolutionary approach, more HM responses (Cosmides & Tooby, 2000) are predicted when p is threatening, whereas (...) decision theory predicts fewer. All 3 experiments were consistent with decision theory. Other theories are discussed, and it is concluded that they cannot account for the behavior observed in these experiments. (shrink)

The increasing availability of passively observed data has yielded a growing interest in “data fusion” methods, which involve merging data from observational and experimental sources to draw causal conclusions. Such methods often require a precarious tradeoff between the unknown bias in the observational dataset and the often-large variance in the experimental dataset. We propose an alternative approach, which avoids this tradeoff: rather than using observational data for inference, we use it to design a more efficient experiment. We consider the case (...) of a stratified experiment with a binary outcome and suppose pilot estimates for the stratum potential outcome variances can be obtained from the observational study. We extend existing results to generate confidence sets for these variances, while accounting for the possibility of unmeasured confounding. Then, we pose the experimental design problem as a regret minimization problem subject to the constraints imposed by our confidence sets. We show that this problem can be converted into a concave maximization and solved using conventional methods. Finally, we demonstrate the practical utility of our methods using data from the Women’s Health Initiative. (shrink)