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Complexity of the problem of choosing among uncertain acts is a salient feature of many of the environments in which departures from expected utility theory are observed. I study a class of Generalized Simple Bounds preferences in which acts that are complex from the perspective of the decision maker are bracketed by "simple" acts to which they are related by statewise dominance. I then study a refinement of the model in which the size of the partition with respect to which an act is measurable arises endogenously as a measure of subjective complexity. Finally, I consider choice behavior characterized by a "cautious completion" of Simple Bounds preferences, and discuss the relationship between this model and models of ambiguity aversion. I develop general comparative statics results, and explore applications to portfolio choice and insurance choice. • Problems of choice problems under uncertainty are complex. • From behavioral axioms, I characterize the set of acts that are well-understood. • Decision makers use acts they understand well to bracket those they do not. • The model is tractable, and admits rich comparative statics. • The model helps explain observed choice patterns in applications. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) projects are mostly based on semi-empirical decisions, emphasising the importance of the structure and lacking a rational comparison of the benefits and costs. The present work offers guidance to overcome this, based on an objective framework using the quantification of the value of SHM in an engineering context. Firstly, procedures for practising engineers are outlined on the basis of the COST guidelines. Secondly, a case study, focused on the reliability of a historic masonry structure, demonstrates the optimisation of surveys based on non-destructive tests calibrated by destructive tests. Both the outlined procedures and case study are carefully prepared and in tune, so the reader can easily understand the feasibility of the framework. Decisions on the utilisation of SHM in practical applications can be effectively achieved based on the highest expected utility gained by SHM. For this, two scenarios are needed: (i) a scenario with at least one SHM strategy and (ii) a scenario without any SHM. [ABSTRACT FROM AUTHOR]

Pascal's wager is one of the most influential arguments in philosophy and decision theory. This paper reformulates Pascal's wager in terms of two-outcome finite payoffs (one before death and one after death). The proposed reformulation accentuates the lexicographic nature of decision maker's preferences. Lexicographic preferences violate the continuity axiom—a standard assumption of many theories of decision making under risk and uncertainty. Since Pascal's wager assumes lexicographic (i.e., discontinuous) preferences, it is appropriate to represent the latter with lexicographic utility and not conventional expected utility theory. [ABSTRACT FROM AUTHOR]

We interrogate mathematical modelling as an instrument of knowledge co-production by concentrating on the classical probabilistic operationalization of decision-making under uncertainty used for informing climate change mitigation options. We construct our co-productive assessment framework by first retrieving criticisms targeted at expected utility theory in relation to its epistemic and ethical limits in dealing with 'true' uncertainty. We then reflect on how ethical values should operate in relation to uncertainty in order to live up to the co-production ideal and specifically, to the principle of Responsible Research and Innovation. We thus undertake the perspective of a general modeller and test our reflections by imagining the classical probabilistic space of calculation as a space of negotiation between probabilities, ideas, values and beliefs. We thus propose an alternative 'public' space of calculation in which the conditions for co-production are set up on a pragmatic and moral account of rational expectations. [ABSTRACT FROM AUTHOR]

Evidential reasoning (ER) rule has been widely used in addressing uncertainty, ignorance, and vagueness information. To explore its performance measure (PM), the perturbation analysis (PA) for the ER rule (ER rule-PA) is conducted, with perturbation taken into consideration. This article aims to analyze the robustness and stability of the ER rule, serving as theoretical basis and technical support for applied research and applications. The combination of two pieces of independent evidence is discussed, and perturbation is added to one piece of evidence. To represent the expected utility of evidence combination under perturbation, perturbation utility is introduced. The novel concept of perturbation coefficient is proposed to characterize the PM of the ER rule (ER rule-PM). The properties of perturbation coefficient are explored to demonstrate the impact of perturbation. The maximum permissible error (MPE) of perturbation coefficient is defined to characterize the acceptability of perturbation. A numerical study is examined to illustrate the implementation process of ER rule-PA. Moreover, a case study of reliability evaluation of aerospace relay is conducted to show the potential applications of ER rule-PA, which makes the proposed method more practical. [ABSTRACT FROM AUTHOR]

The venture capital industry relies extensively on convertible contracts that allow VCs to convert their investments into an equity stake or a fixed debt position at a future date. We study convertible venture investments exposed to failure risk and valuation uncertainty using a double-hazard framework in which venture capitalists maximize the expected utility of their return from the convertible contract, the equity division's determination takes into account the noisy valuation relation of venture profits to venture value, and entrepreneurs search for the best funding deal. These aspects of the model lead to new insights on how important venture characteristics affect key venture finance outcomes and the return-structure of the venture capital market. Model results show analytically that the expected return of convertible investments increases with growth prospects, funding size, initial value and VC productivity, but declines with failure risk, venture horizon and entrepreneur's productivity. The model and numerical study further show that VCs with higher funding capacity will prefer to fund at later stages, as their expected return increases with investment size and competitive searching leads to an equilibrium in which VCs with lower productivities can coexist profitably as their expected return rises. [ABSTRACT FROM AUTHOR]

A central tenet of behavioral economics is that the axioms producing expected utility maximization by consumers are too strong to be descriptive of rational behavior. The existing theory of monetary services aggregation under risk assume expected utility maximization. We extend those results to uncertainty under weaker axiomatic assumptions by using Choquet expectations. Choquet integration reduces to Riemann integration as a special case under the stronger assumption of additive probability measure, not accepted in the literature on behavioral economics. Our theoretical results on monetary services aggregation are generalizations of prior results, nested as special cases of our results under stronger behavioral assumptions. [ABSTRACT FROM AUTHOR]

Ellsberg thought experiments and empirical confirmation of Ellsberg preferences pose serious challenges to subjective expected utility theory (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions under uncertainty which satisfactorily copes with the Ellsberg paradox and other puzzles of SEUT. We apply here the quantum-theoretic framework to the Ellsberg two-urn example, showing that the paradox can be explained by assuming a state change of the conceptual entity that is the object of the decision (decision-making, or DM, entity) and representing subjective probabilities by quantum probabilities. We also model the empirical data we collected in a DM test on human participants within the theoretic framework above. The obtained results are relevant, as they provide a line to model real life, e.g., financial and medical, decisions that show the same empirical patterns as the two-urn experiment. [ABSTRACT FROM AUTHOR]

In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets p increases at the same rate as the sample size n such that their ratio p/n approaches a positive constant c ∈ (0,1) as n → ∞. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S&P 500 constituents. [ABSTRACT FROM AUTHOR]

We report the results of an experiment eliciting individuals' attitudes toward risk and model uncertainty. Using a joint elicitation procedure, we then precisely quantify the strength of individuals' attitude toward ambiguity in the context of the smooth model and characterize its main properties. Our results provide empirical evidence of decreasing absolute ambiguity aversion (DAAA) and constant relative ambiguity aversion (CRAA). These results shed new light on the way ambiguity attitudes may affect important decisions, such as the choice of health insurance policies or the optimal investment strategy in the face of climate change. [ABSTRACT FROM AUTHOR]

• Subjects respond in a pessimistic/averse manner to the uncertainty surrounding climate change and climate change catastrophes, with 67% of subjects successfully purchasing the climate change insurance in the base treatment. • When subjects have more information about the growing frequency of such events, 79% successfully ensure themselves. • A lemons problem may arise with only high-risk individuals/regions subscribing towards climate change insurance and suggests that government intervention may be required to ensure market failures do not arise. • When the strategic uncertainty of coordination with another person is removed, 81% of subjects are successful in buying the insurance. • An indirect intervention in the form of a nudge was unsuccessful, with only 58% of subjects successfully buying the insurance. This paper attempts to study how individuals respond to the availability of an insurance that would safeguard their interests if a climate change catastrophe occurred. If such an insurance is available to them, do individuals insure themselves sufficiently? Further, the study investigates if information regarding the past occurrence of the catastrophic event leads to an increase in insurance subscriptions and/or the emergence of a lemons market. Finally, policy implications are investigated - Can an indirect intervention in the form of a "nudge" ensure a better outcome? [ABSTRACT FROM AUTHOR]

We apply the information gap approach to resource allocation under Knightian (non-probabilistic) uncertainty in order to study how best to allocate public resources between competing defence measures. We demonstrate that when determining the level and composition of defence spending in an environment of extreme uncertainty vis-a-vis the likelihood of armed conflict and its outcomes, robust-satisficing-expected utility will usually be preferable to expected utility maximisation. Moreover, our analysis suggests that in environments with unreliable information about threats to national security and their consequences, a desire for robustness to model misspecification in the decision-making process will imply greater expenditure on certain types of defence measures at the expense of others. Our results also provide a positivist explanation of how governments seem to allocate security expenditures in practice. [ABSTRACT FROM AUTHOR]

• We derive the value of travel time information in very general setting. • Value increases with information quality. • Predictable travel time variability may be costly. • Examples show analytic calculation of value of travel time information. • Results facilitate design and analysis of information policies. In this paper, we derive the value of a signal obtained by a traveller prior to the choice of departure time. The signal does not have to be a perfect prediction of the travel time. It is sufficient that it carries information about the travel time. The traveller may then consider the distribution of travel time conditional on the signal to increase her expected utility by making a better informed choice of departure time. We show that a signal always increases the expected utility compared to the situation without any signal. For a broad class of signals, the expected utility is monotone with respect to signal strength. Furthermore, we demonstrate that even perfect travel time information does not necessarily eliminate the cost of travel time variability and we establish necessary and sufficient conditions for when it does. We find that the predictable part of travel time variability may or may not be costly, depending on the shape of the traveller's scheduling utility at the origin of the trip. Using estimates of scheduling preferences from the literature, we show that the cost of predictable travel time variability may constitute a substantial part of the total cost of travel time variability. In a particular case of scheduling preferences, travel time distribution and noise distribution, we establish an analytic relationship between the strength of the signal and the expected utility of the trip and evaluate the marginal cost of signal weakness. This knowledge may facilitate design and cost-benefit analysis of traveller information systems and policies decreasing travel time variability. [ABSTRACT FROM AUTHOR]

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage's postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. [ABSTRACT FROM AUTHOR]

We study a general robust utility maximization problem from terminal wealth and consumption under state constraints. Our framework includes financial models with constrained portfolios, labor income and large investor models. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle. [ABSTRACT FROM AUTHOR]

Vehicular fog computing has emerged as a cost-efficient solution for task processing in vehicular networks. However, how to realize effective server recruitment and reliable task offloading under information asymmetry and uncertainty remains a critical challenge. In this paper, we adopt a two-stage task offloading framework to address this challenge. First, we propose a convex–concave-procedure-based contract optimization algorithm for server recruitment, which aims to maximize the expected utility of the operator with asymmetric information. Then, a low-complexity and stable task offloading mechanism is proposed to minimize the total network delay based on the pricing-based matching. Furthermore, we extend the work to the scenario of information uncertainty and develop a matching-learning-based task offloading mechanism, which takes both occurrence awareness and conflict awareness into consideration. Simulation results demonstrate that the proposed algorithm can effectively motivate resource sharing and guarantee bounded deviation from the optimal performance without the global information. [ABSTRACT FROM AUTHOR]

Modern theories of decision-making typically model uncertainty about decision options using the tools of probability theory. This is exemplified by the Savage framework, the most popular framework in decision-making research. There, decision-makers are assumed to choose from among available decision options as if they maximized subjective expected utility, which is given by the utilities of outcomes in different states weighted with subjective beliefs about the occurrence of those states. Beliefs are captured by probabilities and new information is incorporated using Bayes' Law. The primary concern of the Savage framework is to ensure that decision-makers' choices are rational. Here, we use concepts from computational complexity theory to expose two major weaknesses of the framework. Firstly, we argue that in most situations, subjective utility maximization is computationally intractable, which means that the Savage axioms are implausible. We discuss empirical evidence supporting this claim. Secondly, we argue that there exist many decision situations in which the nature of uncertainty is such that (random) sampling in combination with Bayes' Law is an ineffective strategy to reduce uncertainty. We discuss several implications of these weaknesses from both an empirical and a normative perspective. This article is part of the theme issue 'Risk taking and impulsive behaviour: fundamental discoveries, theoretical perspectives and clinical implications'. [ABSTRACT FROM AUTHOR]

The predictive power of cumulative prospect theory and expected utility theory is typically compared using decisions from description, where lotteries' outcome values and probabilities are explicitly stated. In decisions from experience, individuals sample (in the sampling paradigm without cost) from the return distributions to learn outcome values and their relative frequencies; here cumulative prospect theory and expected utility theory require the calculation of probabilities from experience. Individuals, however, may be more attuned to the experienced moments of outcome distributions, rather than the probabilities. We therefore test the mean-variance-skewness model, and retrieve the proportion of expected utility theory (over income), cumulative prospect theory, and mean-variance-skewness populations using a latent-class hierarchical Bayesian model across six large datasets. For simple lotteries (with 1-2 outcomes), we find a mixture of cumulative prospect theory and mean-variance-skewness populations in decisions from both description and experience. For more complex lotteries (with 2-3 outcomes), all participants are classified as cumulative prospect theory types in decisions from description, but as mean-variance-skewness types in decisions from experience. This suggests that in decisions from experience with more complex return distributions, preferences for skewness are more predictive than nonlinear probability weighting. [ABSTRACT FROM AUTHOR]

At least since Leonard Savage's extension of von Neumann and Morgenstern's expected utility, rational choice theory has been interpreted as a theory prescribing what individuals should do in any decision context, ranging from certainty to risk and uncertainty. After decades this received view, usually termed Bayesian, has been criticized for its normative content. This paper compares the current critique of the notion of Bayesian rationality, proposed by Itzhak Gilboa, with Daniel Ellsberg's classic critique of Savage's understanding of rationality. The paper argues that Ellsberg's classic analysis of Savage's theory totally anticipated today's criticism. [ABSTRACT FROM AUTHOR]

This paper studies n -player games where players' beliefs about their opponents' behavior are capacities (fuzzy measures, non-additive probabilities). The concept of an equilibrium under uncertainty was introduced by J. Dow and S. Werlang [5] for two players and was extended to n -player games by J. Eichberger and D. Kelsey [8] . Expected utility was expressed by Choquet integral. We consider the concept of an equilibrium under uncertainty in this paper but with expected utility expressed by Sugeno integral. Existence of such an equilibrium expressed by possibility (or necessity) capacities is demonstrated using some abstract non-linear convexity on the space of capacities. [ABSTRACT FROM AUTHOR]

In this article, we study a robust optimal investment and reinsurance problem for a general insurance company which holds shares of an insurance company and a reinsurance company. Assume that the claim process described by a Brownian motion with drift, the insurer can purchase proportional reinsurance, and both the insurer and the reinsurer can invest in a risk-free asset and a risky asset. Besides, the general insurance company’s manager is an ambiguity-averse manager (AAM) who worries about model uncertainty in model parameters. The AAM’s objective is to maximize the minimal expected exponential utility of the weighted sum surplus process of the insurer and the reinsurer. By using techniques of stochastic control theory, we first derive the closed-form expressions of the optimal strategies and the corresponding value function, and then the verification theorem is given. Finally, we present numerical examples to illustrate the effects of model parameters on the optimal investment and reinsurance strategies, and analyze utility losses from ignoring model uncertainty. [ABSTRACT FROM PUBLISHER]

In many parts of the world, conservation successes or global anthropogenic changes have led to increasing native species populations that then compete with human resource use. In the Orkney Islands, Scotland, a 60-fold increase in Greylag Goose Anser anser numbers over 24 years has led to agricultural damages and culling attempts that have failed to prevent population increase. To address uncertainty about why populations have increased, we combined empirical modelling of possible drivers of Greylag Goose population change with expert-elicited benefits of alternative management actions to identify whether to learn versus act immediately to reduce damages by geese. We built linear mixed-effects models relating annual goose densities on farms to land-use and environmental covariates and estimated AICc model weights to indicate relative support for six hypotheses of change. We elicited from experts the expected likelihood that one of six actions would achieve an objective of halting goose population growth, given each hypothesis for population change. Model weights and expected effects of actions were combined in Value of Information analysis (VoI) to quantify the utility of resolving uncertainty in each hypothesis through adaptive management and monitoring. The action with the highest expected value under existing uncertainty was to increase the extent of low quality habitats, whereas assuming equal hypothesis weights changed the best action to culling. VoI analysis showed that the value of learning to resolve uncertainty in any individual hypothesis for goose population change was low, due to high support for a single hypothesis of change. Our study demonstrates a two-step framework that learns about the most likely drivers of change for an over-abundant species, and uses this knowledge to weight the utility of alternative management actions. Our approach helps inform which strategies might best be implemented to resolve uncertainty when there are competing hypotheses for change and competing management choices. [ABSTRACT FROM AUTHOR]

We use a framed field experiment considering hypothetical stocking rate decisions made by grazing enterprise managers and estimate non-linear multinomial logit models for a range of nested non-expected utility and expected utility models. The risk and decision-bias parameters for five models estimated for individual responses are shown to be significantly related to land condition but in ways which suggest behavioural aspects of decision making are critical in understanding land management and stocking rate decisions. Our results show that individual heterogeneity in decision making amongst farming groups is likely to be a significant source of variation in farming intensity and technology adoption decisions. This heterogeneity does not appear to be a reflection of socio-demographic characteristics. Furthermore, decision functions appear to be biased toward selection of simpler representative functions (e.g. Expected Utility) for sample averages. This suggests that experimental findings that Expected Utility is representative for actual decisions may be due to sample averaging rather than reflect actual behaviour. [ABSTRACT FROM AUTHOR]

I study the implications of Wald's (1947) complete class theorem for decision making under Knightian uncertainty (or ambiguity). Suppose we call someone who uses Wald's approach to statistical decision making a Waldian. A Waldian may then have preferences over acts that are not in agreement with subjective expected utility but always chooses as if she was a subjective expected utility maximizer. In particular, even Wald's (1945) minmax decision rule is consistent with subjective expected utility. [ABSTRACT FROM AUTHOR]

This paper examines climate-change benefit-cost analysis in the presence of scientific uncertainty in the form of ambiguity. The specific issue addressed is the robustness of benefit-cost analyses of climate-change policy alternatives to relaxation of Savage's original axioms. Two alternatives to subjective expected utility (SEU) are considered: maximin expected utility (MEU) and incomplete expected utility (IEU). Among other results, it is demonstrated that polar opposite recommendations can emerge in an ambiguous decision setting even if all agree on Society's rate of time preference, Society's risk attitudes, the degree of ambiguity faced, and the scientific primitives. We show that, for a simple numerical simulation of our model, an MEU decision maker favors policies which immediately tackle climate change while an IEU decision prefers “business as usual”.“Each agency shall assess the costs and benefits of the intended regulation, and recognizing that some costs and benefits are difficult to quantify, propose or adopt a regulation only upon a reasoned determination that the benefits of the intended regulation justify its cost.” Executive Order 12866 of the US President. [ABSTRACT FROM AUTHOR]

In this article, a new model for decision making under uncertainty is presented. Here, we model human attitude toward risks to show that an individual estimate of the expected utility of a lottery follows a generalized Beta distribution with a random error that follows a similar distribution. An individual is said to maximize his stochastic utility when requested to present his preference between risky lotteries. Hypothetically, risky lotteries are those exhibiting wider ranges of rewards where human estimate will not be below the utility of the lowest reward nor above the highest of the lottery. The Beta distribution is bounded and complies to such intuitive preconditions with a variance depending on such bounds. The proposed model will overestimate/underestimate the expected utility of a lottery according to the lottery probability mass and individuals' risk attitudes. By such estimation, our model conforms to the fourfold choice pattern. The model also explains the violations present as inconsistencies in the expected utility theory, such as Allais paradox, common consequence effect, common ratio effect, and the violation of betweenness that can be found in the fourfold choice pattern. For the validation purposes, 13 datasets from literature were collected and tested. The β-SU model fits the data at least as good as other approaches such as the CPT/StEUT and presents higher prediction log-likelihoods and less sum of squared errors in most of the cases, a matter that supports the proposition that human estimates of the expected utility may be drawn out of a generalized Beta distribution. [ABSTRACT FROM AUTHOR]

Risk is caused by the uncertainty of state of nature and a decision maker's selection, and the result may appear to be an unfavorable outcome. Therefore, a decision maker wants to maximize an expected return with minimal risk exposures. In this paper, we propose an expected utility and uncertainty risk (EU-UR) model based on the reference prior, which extends the classical decision model under uncertainty. The EU-UR model is made by making a compromise between measures of expected utility and uncertainty. The model is empirically validated by applying to the Levy's case and the Allais paradox. [ABSTRACT FROM AUTHOR]

This article examines the role of risk aversion on the sustainable management of mixed fisheries. We consider a bio-economic model of multiple species harvested by a single fleet with uncertain costs of effort. We assume that the regulatory agency aims at reaching MMEY (Multispecies Maximum Economic Yield) by maximizing the expected utility of total profits, where the utility function captures risk aversion. We show analytically that such a risk-averse MMEY mitigates the risk of biological and economic overexploitation of the different species and thus of biodiversity loss. However excessively high risk aversion also may also lessen food production at MMEY. Thus, risk aversion implies a trade-off between different bio-economic goals. These findings are illustrated with the case study of the Australian South East Fishery, where intermediate risk aversion levels allow for balanced bio-economic management objectives, therefore fostering sustainability. [ABSTRACT FROM AUTHOR]

Abstract: We add some elements of prospect theory to an analytically tractable version of Lucas''s “islands” model and show that the inclusion of reference dependence, declining sensitivity and loss aversion into the agents’ utility function leads to four main results. First, the presence of behavioral elements negatively affects the natural level of output. Second, loss aversion reduces output variance. Third, the expected utility of a representative agent is generally lower than that obtained when loss aversion is absent. Fourth, the presence of loss aversion eliminates the paradoxical increase in expected utility that may be generated, in the standard model, by an increase in monetary policy uncertainty. [Copyright &y& Elsevier]

Abstract: Recent changes in the assessment and management of risks has had the effect that greater importance has been placed on relationships between individuals and within groups to inform decision making. In this paper, we provide the theoretical underpinning for an expected utility approach to decision-making. The approach, which is presented using established evidence support logic (TESLA™), integrating the expected utilities in the forming of group decisions. The rationale and basis are described and illustrated through a hypothetical decision context of options for the disposal of animal carcasses that accumulate during disease outbreaks. The approach forms the basis for exploring the richness of risk-based decisions, and representing individual beliefs about the sufficiency of evidence they may advance in support of hypotheses. [Copyright &y& Elsevier]

Abstract: Most welfare models of environmental or mortality risk reductions assume that risks are exogenously determined and known with certainty. However, a growing body of research suggests that uncertainty about risks can affect choices over risky prospects. I present a decision-weighted random-utility model that decomposes welfare losses into those attributable to an increase in the deterministic component of risk and those attributable to uncertainty about risk. I apply the model to an illustrative dataset of subjects'' perceived mortality risk and willingness to accept the risk of nuclear-waste transport. I estimate the model using Lewbel''s (2000) strictly exogenous regressor approach to account for endogeneity bias and measurement error. Subjects display aversion to both risk and uncertainty about the risk of a transport accident, so that increases in either leads to social-welfare losses. Roughly 12% of the external cost of nuclear-waste transport is attributable to the public''s uncertainty about transport risk. [Copyright &y& Elsevier]

Abstract: We consider a decision maker facing uncertainty which behaves as a subjective expected utility maximizer. The value of information is traditionally captured as a greater expected utility the decision maker can achieve by selecting a best strategy as information arrives. We deal with the limit process of being better informed, and introduce an information density function depending solely on the states that gives an exact least upper bound to being more informed. This information density function is given by a Radon–Nikodym-type theorem for set functions and is explicitly computed for the countable case. [Copyright &y& Elsevier]

The novel research paradigm, dubbed the “court of miracles of hydrological modelling”, focuses on achieving scientific progress in circumstances which traditionally would be called model failures. Many of the associated modelling issues can be addressed systematically and coherently within the mathematical framework of Bayesian forecast-decision theory. Five of them are addressed herein: (a) choosing a criterion function for making rational decisions under uncertainty (a meta-decision problem); (b) modelling stochastic dependence between variates to quantify uncertainty and predict realizations; (c) fusing data from asymmetric samples to cope with unrepresentativeness of small samples and corruptive effects of outliers; (d) calibrating probabilistic predictions against a prior distribution; and (e) ordering predictors, or models, in terms of their informativeness (equivalently, in terms of their economic value to a decider). It is suggested that communication between hydrologists and deciders (planners, engineers, operators of hydrosystems) would benefit if hydrologists adopted, at least on some issues, the perspective of deciders, who must act in a timely and rational manner, and for whom hydrological estimates and predictions have economic consequences. Citation Krzysztofowicz, R. (2010) Decision criteria, data fusion and prediction calibration: a Bayesian approach. Hydrol. Sci. J. 55(6), 1033-1050. [ABSTRACT FROM AUTHOR]

Why would people pay more for a $50 gift certificate than for the opportunity to receive a gift certificate worth either $50 or $100, with equal probability? This article examines three possible mechanisms for this recently documented uncertainty effect (UE): First, awareness of the better outcome may devalue the worse one. Second, the UE may have arisen in the original demonstration of this effect because participants misunderstood the instructions. Third, the UE may be due to direct risk aversion, that is, actual distaste for uncertainty. In Experiment 1 , the UE was observed even though participants in the certainty condition were also aware of the better outcome; this result eliminates the first explanation. Experiment 2 shows that most participants understand the instructions used in the original study and that the UE is not caused by the few who do not. Overall, the experiments demonstrate that the UE is robust, large (prospects are valued at 65% of the value of the worse outcome), and widespread (at least 62% of participants exhibit it). [ABSTRACT FROM AUTHOR]

Abstract: Although the expected effects of environmental policies and interventions are rarely known with certainty, stated preference surveys rarely elicit preferences over uncertain environmental outcomes. This article presents empirical results challenging the view that ignoring such uncertainty during preference elicitation is of no consequence so long as people only care about final environmental states. We show that measured preferences for final environmental states, water quality in this case, depend on whether people choose between final states or between lotteries over final states. In contrast to the typical finding for monetary lotteries, we find significant under-weighting of low probability events related to water quality. [Copyright &y& Elsevier]

Real decision makers (DM) partially quantify uncertainty as probability uncertainty intervals. Then alternatives are modeled as fuzzy-rational lotteries. Those can be approximated by standard lotteries with point-estimate probabilities, referred as classical-risky. Ranking the approximating classical-risky lotteries is a problem under risk, solved by expected utility. However, the approximation itself is a problem under strict uncertainty. Here this part of the problem is solved by criteria under strict uncertainty, which if not perfectly rational, are well worked descriptive methods with known properties. The proposed Laplace, Wald, maximax and Hurwiczα expected utility criteria for prescriptive ranking of fuzzy-rational lotteries allow the DM to control the approximation of alternatives with partially quantified uncertainty in consistency with her/his degree of belief and with his optimism-pessimism attitude. That makes them superior to the widespread abandoned-m and normalized mean criteria, which often violate the intrinsic subjective probabilities of the DM. The proposed criteria are generalizations of expected utility criterion under risk and of their standard versions under strict uncertainty. [ABSTRACT FROM AUTHOR]

Moral theory has mostly focused on idealized situations in which the morally relevant properties of human actions can be known beforehand. Here, a framework is proposed that is intended to sharpen moral intuitions and improve moral argumentation in problems involving risk and uncertainty. Guidelines are proposed for a systematic search of suitable future viewpoints for hypothetical retrospection. In hypothetical retrospection, a decision is evaluated under the assumption that one of the branches of possible future developments has materialized. This evaluation is based on the deliberator’s present values, and each decision is judged in relation to the information available when it was taken. The basic decision rule is to choose an alternative that comes out as morally acceptable (permissible) from all hypothetical retrospections. [ABSTRACT FROM AUTHOR]

In economics, the prevailing framework to explain preferences under uncertainty is the Expected Utility theory. Despite its widespread use, the Expected Utility theory is not free from problems. Experimental and empirical works shows that, in real life, the choices of individuals among risky alternatives conflict with the axioms of the Expected Utility theory. Preferences Under Uncertainty and the Deficiencies of the Expected Utility Model. [ABSTRACT FROM AUTHOR]

Many quantitative scales are constructed using cutoffs on a continuum with scores assigned to the cutoffs. This paper develops a framework for using or constructing such scales from a decision-making standpoint. It addresses questions such as: How many distinct thresholds or cutoffs on a scale (i.e., what levels of granularity) are useful for a rational agent? Where should these thresholds be placed given a rational agent’s preferences and risk-orientation? Do scale score assignments have any bearing on decision-making and if so, how should scores be assigned? Given two possible states of nature $$\{A, \sim A\}$$ , an ordered collection of alternatives $$\{R_{0}, R_{1},{\ldots}, R_{K}\}$$ from which one is to be selected depending on the probability that A is the case, a simple expected utility condition stipulates when adjacent alternatives are distinguishable and determines the threshold odds separating them. Threshold odds and utilities are mapped onto scale scores via a simple distance model. The placement of the thresholds reflects relative concern over decisional consequences given A versus consequences given ∼ A. Likewise, it is shown that scale scores reflect risk-aversion or risk-seeking not only with respect to A versus ∼ A but also with respect to the rank of the R j . Connections are drawn between this framework and rank-dependent expected utility (RDEU) theory. Implications are adumbrated for both machine and human decision-making. [ABSTRACT FROM AUTHOR]

This article analyzes a general model of religious choice under uncertainty by interpreting Pascal's wager as an expected utility problem and faith as insurance. The authors assert that the basic religious choice is one of faith and that religious practice is essentially the allocation of time required to maintain a level of faith in an uncertain environment. The optimal amount of faith and hence the optimal amount of religious practice are determined in part by the costs of maintaining faith, which depend on, among other things, the level of religious capital. The solution to the expected utility problem yields several interesting predictions regarding both the high percentage of individuals choosing at least some positive level of faith and the variation in faith levels across individuals. A series of regressions provide evidence indicating general support for the main predictions of the model. [ABSTRACT FROM AUTHOR]

Expected utility theory tells us how we should make decisions under uncertainty: we should choose the option that leads to the greatest expectation of utility. This may, however, not be the option that is likely to produce the best result – that may be the wrong choice if it also creates a small chance of a great disaster. A small chance of disaster may be the most important consideration in decision making. Climate change creates a small chance of disaster, and some authors believe this to be the most important consideration in deciding our response to climate change. To know whether they are right, we need to make a moral judgement about just how bad the disaster would be. [ABSTRACT FROM PUBLISHER]