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Overconfidence is pervasive in subjective probability distributions (SPDs). We develop new methods to analyze judgments that entail both a distribution of possible outcomes in a population (aleatory uncertainty) and imperfect knowledge about that distribution (epistemic uncertainty). In four experiments, we examine the extent to which subjective probability mass is concentrated in a small portion of the distribution versus spread across all possible outcomes. We find that although SPDs roughly match the concentration of the empirical, aleatory distributions, people's judgments are consistently overconfident because they fail to spread out probability mass to account for their own epistemic uncertainty about the location and shape of the distribution. Although people are aware of this lack of knowledge, they do not appropriately incorporate it into their SPDs. Our results offer new insights into the causes of overconfidence and shed light on potential ways to address this fundamental bias. This paper was accepted by Yuval Rottenstreich, behavioral economics and decision analysis. Funding: Support for this research was provided by the Fuqua School of Business at Duke University and the Haas School of Business at the University of California at Berkeley. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2019.00660. [ABSTRACT FROM AUTHOR]

This paper presents a new representation of preference orderings for the study of ambiguity-related decision-making. The central feature is a preference-based decomposition of subjective probabilities that provides information about inherent ambiguity. The probability decomposition is combined with a utility function reflecting the decision-maker's attitude toward ambiguity. The proposed theory generalizes Savage's SEU and allows for a straightforward measurement of ambiguity and ambiguity aversion while keeping concepts for measuring risk and risk attitudes unaffected. For the measurement of ambiguity, concepts of probability theory can be used since decision acts can be interpreted as two-dimensional probability distributions. The proposed measure of ambiguity aversion exploits the properties of the utility function in the same way as the Arrow/Pratt measure of risk aversion. [ABSTRACT FROM AUTHOR]

Implied subjective probabilities from futures wagering markets are typically determined using a system known as "fair odds." Here, an alternative system of calculating subjective probabilities—"quasi‐parimutuel"—is offered. Instead of considering individual lines independent of the remainder of the wagering opportunities, the quasi‐parimutuel method considers the ratios of wagers required between lines such that a constant return is generated for every line. As a result, relative to the fair odds system, favorites (underdogs) have higher (lower) subjective probabilities, and expected returns across all wagers vary. [ABSTRACT FROM AUTHOR]

Although the subjective expected utility (SEU) theory is more than 60 years old, it was recently discovered by Hartmann (Econometrica 88(1):203–205, 2020, https://doi.org/10.3982/ECTA17428) that one of the original seven postulates is redundant, i.e., it is implied by the other six postulates. In this brief communication, we show that this redundant axiom is the only one that is implied by the other axioms, thereby establishing that the remaining six postulates form an independent axiomatic system. This result further streamlines the preference assumptions underlying the SEU theory. [ABSTRACT FROM AUTHOR]

Lack of sufficient knowledge about flood risk can lead to "don't know" responses or non-response in risk perception surveys, and incorrect treatment of these responses can lead to bias in the results. In this study, we focus on the possibility that the "50%" response actually means "fifty-fifty" and thus reflects epistemic uncertainty in the subjective probability of river flooding. We conduct an analysis that introduces a concomitant-variable latent class model as a method to adjust for this epistemic uncertainty. The results of the analysis accounting for epistemic uncertainty suggest that risk communication, such as simulated evacuation experiences and flood-related information distribution, increases subjective probability. Moreover, the proportion of latent classes with epistemic uncertainty decreased with each successive wave of the survey, thereby suggesting that knowledge acquisition and learning through the demonstration experiment led to a reduction in epistemic uncertainty. The analysis using the evacuation decision-making model also suggested that the introduction of subjective probability contributed to improving the likelihood of the model. These results suggest that knowledge acquisition through risk communication and short-term panel survey can lead to correct risk perception estimations and influence evacuation decisions. [ABSTRACT FROM AUTHOR]

Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of probability. This article aims to separate the concept of probability which is scientifically based from other concepts that do not have this characteristic. The scientifically based concept of probability is Kolmogorov’s concept of probability models together with the conditions of their applicability. Bayesian statistics is based on the subjective concept of probability, and as such can only have a heuristic value in searching for the truth, but it cannot and must not replace the truth. The way out of the crisis should take Kolmogorov and Bayesian analysis as elements, each of which has a well-defined and limited use. Only together with qualitative analysis and other types of quantitative analysis, and combined with experiments, they can contribute to reaching correct conclusions.

This paper studies decision-making in the face of two stochastically independent sources of uncertainty. It characterizes axiomatically a Subjective Expected Utility representation of preferences where subjective beliefs consist of a product probability measure. The two key axioms in this characterization both involve some behavioral notions of stochastic independence. Our result can be understood as a purely subjective version of the Anscombe and Aumann (Ann Math Stat 34:199–205, 1963) theorem that avoids the controversial use of exogenous probabilities by appealing to stochastic independence. We also obtain an extension to Choquet Expected Utility representations. [ABSTRACT FROM AUTHOR]

We prove the existence of an expected utility function for preferences over probabilistic prospects satisfying Strict Monotonicity, Indifference, the Common Ratio Property, Substitution and Reducibility of Extreme Prospects. The example in [1] that is inconsistent with the existence of a von Neumann-Morgenstern for preferences over probabilistic prospects, violates the Common Ratio Property. Subsequently, we prove the existence of expected utility functions with piecewise linear Bernoulli utility functions for preferences that are piece-wise linear. For this case a weaker version of the Indifference Assumption that is used in the earlier existence theorems is sufficient. We also state analogous results for probabilistic lotteries. We do not require any compound prospects or mixture spaces to prove any of our results. In the third last section of this paper, we "argue" that the observations related to Allais paradox, do not constitute a violation of expected utility maximization by individuals, but is a likely manifestation of individuals assigning (experiment or menu-dependent?) subjective probabilities to events which disagree with their objective probabilities. [ABSTRACT FROM AUTHOR]

Evaluative knowledge of an object domain can be represented not only as an objective (statistical) probability, but also as a subjective (expert) probability. Expert evaluations may be incomplete and uncoordinated with each other. An instrument is needed to check the coordination of expert knowledge. The paper presents a formalization of the subjective interpretation of probability in the language of the theory of fuzzy models. This allows us to formulate coordination criteria for evaluative knowledge obtained from experts. Various properties of coordinated evaluative knowledge are described, the concept of a minimal fuzzy model coordinated with a given evaluative knowledge is considered, and the uniqueness criteria for such a model are investigated. [ABSTRACT FROM AUTHOR]

This work was developed at the Dr. Publio Escobar Gómez Hospital in Ecuador. The objective is to reduce pain and tone the abdominal and back muscles in adults with lumbosciatica through the application of hypopressive abdominal training to help reintroduce the adult to their work and social activities. We worked with a population of 25 male and female adult patients, with an age range from 30 to 50 years old. To process the collected data, we determined that classical statistics are too restrictive in terms of the hypotheses to fulfill. For example, the initial evaluation employing the Visual Analogue Scale (VAS) that assesses the intensity of pain is subjective and depends on the pain threshold of each patient, moreover, the size of the population is not large (<30), therefore it is not possible to carry out a study with the rigor required by classical statistics to infer. That is why we have decided to use neutrosophic statistics to process the data, which will consist of pain scales in the form of intervals, which will contain indeterminacy. The statistical test selected was the T-test for paired samples. In addition to the fact that neutrosophic statistics admit the principles of De Finetti's subjective probabilities and the statistics derived from it, where objective evidence through a random sample is not needed to reach valid conclusions. [ABSTRACT FROM AUTHOR]

This paper offers a constructively critical examination of George Shackle's theory of expectations and decision-making under uncertainty, a theory that Shackle developed because he questioned the relevance of objective probabilities as foundations for expectations. His theory is cast in terms of degrees of possibility and potential for surprise associated with disbelief that comes from imagining things that could prevent outcomes from eventuating. His idea that there may be ranges of mutually exclusive "perfectly possible" events has posed a problem for blending his thinking with the subjective probability approach, but here it is argued that this idea is flawed. Shackle's theory of how expectations are deployed in making choices involves a reference-dependent theory of attention that results in focus on best-case and worst-case pairs of outcomes for each scheme. The paper identifies potential synergies with this idea and prospect theory and explores emotion- and satisficing-based perspectives as well as Shackle's formal analysis of how focus outcomes are used in ranking rival schemes of action. [ABSTRACT FROM AUTHOR]

Expert judgment plays an essential role in assessing the safety of levees, since these very long structures are generally old, few data are available for them, and they are subject to complex failure mechanisms. Expert judgement is required to assess the failure probabilities of levees when carrying out risk analysis studies. However, expert judgement is subject to biases that are highly likely to impair the quality of the probabilistic assessments obtained. This article presents a method for reducing biases in expert opinion, illustrated by its application to the case of an existing levee. Initially, the method comprises the calibration of the opinions of a panel of six experts based on the results of a quantitative analysis applied to 30 levee cross-sections for which numerical calculations were performed. It then proposes a procedure to debias expert assessments using bias correction coefficients. Regarding its application, the assessments made by the experts were debiased for 30 calibration variables. The correction coefficients obtained were then applied for the assessment of 10 variables of interest. The results show a significant reduction of biases, associated with a readjustment of the uncertainty intervals given by the experts. [ABSTRACT FROM AUTHOR]

Redundant or excessive information can sometimes lead people to lean on it unnecessarily. Certain experimental designs can sometimes bias results in the researcher’s favor. And, sometimes, interesting effects are too small to be studied, practically, or are simply zero. We believe a confluence of these factors led to a recent paper (Isaac & Brough, 2014, JCR). This initial paper proposed a new means by which probability judgments can be led astray: the category size bias, by which an individual event coming from a large category is judged more likely to occur than an event coming from a small one. Our work shows that this effect may be due to instructional and mechanical confounds, rather than interesting psychology. We present eleven studies with over ten times the sample size of the original in support of our conclusion: We replicate three of the five original studies and reduce or eliminate the effect by resolving these methodological issues, even significantly reversing the bias in one case (Study 6). Studies 7-8c suggest the remaining two studies are false positives. We conclude with a discussion of the subtleties of instruction wording, the difficulties of correcting the record, and the importance of replication and open science.

Rachlin and colleagues laid the groundwork for treating the discounting of probabilistic goods as a variant of the discounting of delayed goods. This approach was seminal for a large body of subsequent research. The present paper finds the original development problematic: In converting probability to delay, the authors incorrectly dropped trial duration. The subsumption of probability by delay is also empirically questionable, as those are different functions of variables such as magnitude of outcome and commodity versus money. A variant of Rachlin's theme treats human discounting studies as psychophysical matching experiments, in which one compound stimulus is adjusted to equal another. It is assumed that a function of amount (its utility) is multiplied by a function of probability (its weight). Conjoint measurement establishes the nature of these functions, yielding a logarithmic transform on amount, and a Prelec function on probability. This model provides a good and parsimonious account of probability discounting in diverse data sets. Variant representations of the data are explored. By inserting the probabilistically discounted utility into the additive utility theory of delay discounting, a general theory of probabilistic intertemporal choice is achieved. [ABSTRACT FROM AUTHOR]

We propose a model of an agent's probability and utility that is a compromise between Savage (The foundations of statistics, Wiley, 1954) and Jeffrey (The Logic of Decision, McGraw Hill, 1965). In Savage's model the probability–utility pair is associated with preferences over acts which are assignments of consequences to states. The probability is defined on the state space, and the utility function on consequences. Jeffrey's model has no consequences, and both probability and utility are defined on the same set of propositions. The probability–utility pair is associated with a desirability relation on propositions. Like Savage we assume a set of consequences and a state space. However, we assume that states are comprehensive, that is, each state describes a consequence, as in Aumann (Econometrica 55:1–18, 1987). Like Jeffrey, we assume that the agent has a preference relation, which we call desirability, over events, which by definition involves uncertainty about consequences. For a given probability and utility of consequences, the desirability relation is presented by conditional expected utility, given an event. We axiomatically characterize desirability relations that are represented by a probability–utility pair. We characterize the family of all the probability–utility pairs that represent a given desirability relation. [ABSTRACT FROM AUTHOR]

This note is devoted to the problem of signaling (marginal inconsistency) in the Bell-type experiments with physical and cognitive systems. It seems that in quantum physics, this problem is still not taken seriously. Only recently have experimenters started to check the signaling hypothesis for their data. For cognitive systems, signaling was statistically significant in all experiments (typically for decision making) performed up to today. Here, one cannot simply ignore this problem. Since signaling contradicts the quantum theory of measurement for compatible observables, its statistical significance in experiments with humans can be considered as an objection for quantum-like modeling—applications of quantum theory to cognition, decision making, psychology, economics and finance, social and political science. In this paper, we point to two possible sources of signaling generation that are consistent with quantum measurement theory. Thus, the signaling objection for quantum-like modeling is not catastrophic. One of these sources is the direct physical signaling about selection of experimental settings, questions or tasks in quantum-like studies. Another possible source is a state modification dependent on experimental settings. The latter was a rather common source of signaling in quantum physics. Since the physical size of the brain is very small comparing with the light velocity, it seems to be impossible to prevent the direct physical signaling (with electromagnetic waves) between the brain's areas processing two questions a and b . However, if, for these questions, not the electromagnetic waves, but electrochemical communication plays the crucial role, the experimenter may hope to make signaling weaker by answering the questions faster. The problem of question-dependent mental state modification seems to be solvable via smarter experimental design. This paper can be useful both for physicists interested in quantum foundations and for researchers working in quantum-like studies, e.g., applying the quantum theory to model decision making or psychological effects. This paper is solely about quantum theory. Thus, we do not consider general contextual probabilistic models. [ABSTRACT FROM AUTHOR]

Copyright of Revue Economique is the property of Fondation Nationale des Sciences Politiques and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The process of revising the Guide to the Expression of Uncertainty in Measurement (GUM) is ongoing. A successful revision must be theoretically sound, so it must be based on a recognized paradigm for scientific data analysis. The major candidate paradigms of statistical inference are the frequentist paradigm — where probability statements are only used to describe the frequency behaviour of processes — and the Bayesian paradigm — where probability statements are also used to describe the degree of belief of the speaker and where the subject of that belief may be the unknown value of a constant. These paradigms are incompatible, and there remains disagreement about which should form the basis of the practical procedures advocated in a revised GUM. This paper uses published results to examine foundational ideas in two different Bayesian approaches, which themselves are inconsistent at a basic, conceptual, level. So-called ‘objective’ Bayesian statistics is based on the premise that a probability distribution can accurately represent a set of information about a constant, which is a premise of the system of analysis currently favoured by the BIPM. This premise is proven to lead to a logical contradiction, which renders the theory untenable. In contrast, subjective Bayesian methods are theoretically satisfactory if they are used in their proper context, which is the context of personal decision-making. But simple examples show that the use of subjective probability in a client-centred measurement can lead to unacceptable results. These examples involve the mixing of epistemic uncertainty (the uncertainty of personal doubt) with aleatory uncertainty (the uncertainty of an unpredictable physical process). They show that these two types of uncertainty cannot always be treated as one, which is a conclusion with profound implications for the role of Bayesian statistics in science. The analysis in this paper also involves a discussion of the ‘meaning’ of probability, which has been a divisive subject for many years. It is argued here that the implied question is inappropriate: the relevant question is not “what does probability mean?” but “what role can probability meaningfully and accurately play?” The results about objective and subjective Bayesian statistics discussed in this paper support the conclusion that a sound and practical system of analysis must be based on the frequency role of probability.

The paper investigates the validity of individual perceptions of heart disease risks, and examines how information and risk perceptions affect marginal willingness to pay (MWTP) to reduce risk, using data from a stated preference survey. Results indicate that risk perceptions held before receiving risk information are plausibly related to objective risk factors and reflect individual-specific information not found in aggregate measures of objective risk. After receiving information, individuals' updates of prior risk assessments are broadly consistent with Bayesian learning. Perceived heart disease risks thus satisfy construct validity and provide a valid basis for inferring MWTP to reduce risk. Consistent estimators of the relationship of MWTP to endogenously perceived risk are developed. Estimating MWTP based on objective rather than subjective risks causes misleading inferences about benefits of risk reduction. An empirical case study shows that estimated benefits may be as much as 60–98 % higher when estimated using individuals' heterogeneous perceptions of risk than when using aggregate estimates of objective risk. The main contributions include assessing the validity of risk perceptions and their updating, consistently estimating the relationship between MWTP and endogenously perceived risk, and demonstrating the importance of employing risk perception information for accurate benefit measurement. [ABSTRACT FROM AUTHOR]

Copyright of Procesos de Mercado is the property of Procesos de Mercado. Revista Europea de Economia Politica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper I model a decision maker who forms beliefs and opinions using a dialectic heuristic that depends on their degree of skepticism or credulity. In an application to political spin, two competing parties choose how to frame commonly observed evidence. If the receiver is sufficiently credulous, equilibrium spin is maximally extreme and generates short, superficial news cycles. When receivers vary in their skepticism, there is partisan sorting by skepticism parameter: the more credulous group systematically favors one party and displays hostility to evidence and a media they see as biased. In behavioral applications in which the frames arise from the decision maker's internal deliberation, a decision maker with the same credulous nature would display known behavioral anomalies in forming beliefs and forming decision weights from stated probabilities. The dialectic model therefore captures a simple psychological mechanism and matches closely some stylized facts across these three disparate applications. [ABSTRACT FROM AUTHOR]

An aspect of Peirce's thought that might still be underappreciated is his resistance to what Levi calls pedigree epistemology, i.e., to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce's criticisms of subjectivism, to the extent that they grant that such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the context of probabilistic epistemology, however, does challenge prominent subjectivist responses to the problem of the priors. [ABSTRACT FROM AUTHOR]

According to an infinite frequency principle, it is rational, under certain conditions, to set your credence in an outcome to the limiting frequency of that outcome if the experiment were repeated indefinitely. I argue that most infinite frequency principles are undesirable in at least one of the following ways: (1) accepting the principle would lead you to accept bets with sure losses, (2) the principle gives no guidance in the case of deterministic experiments like coin tosses and (3) the principle relies on a metaphysical property, ‘chanciness’, whose necessary and sufficient conditions are unknown. I show that a frequency principle that is based on the principal principle suffers from problems related to the definition of ‘chance’ or ‘chanciness’, which could lead to all three of the above problems. I introduce a version of the infinite frequency principle that does not rely on a notion of chance or chanciness and does not suffer from any of these problems. [ABSTRACT FROM AUTHOR]

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold beliefs of both types simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List. The nature, relevance, and implications of the tension are explained and assessed. [ABSTRACT FROM AUTHOR]

Despite widespread exposure to substantial medical expenditure risk in low-income populations, health insurance enrollment is typically low. This is puzzling from the perspective of expected utility theory. To help explain it, this paper introduces a decomposition of the stated willingness to pay (WTP) for insurance into its fair price and three behavioral deviations from that price due to risk perception and risk attitude consistent with prospect theory, plus a residual. To apply this approach, we elicit WTP, subjective distributions of medical expenditures and risk attitude (utility curvature and probability weighting) from Filipino households in a nationwide survey. We find that the mean stated WTP of the uninsured is less than both the actuarially fair price and the subsidized price at which public insurance is offered. This is not explained by downwardly biased beliefs: both the mean and the median subjective expectation are greater than the subsidized price. Convex utility in the domain of losses pushes mean WTP below the fair price and the subsidized price, and the transformation of probabilities into decision weights depresses the mean further, at least using one of two specific decompositions. WTP is reduced further by factors other than risk perception and attitude. [ABSTRACT FROM AUTHOR]

An honest communication of uncertainty about quantities of interest enhances transparency in scientific assessments. To support this communication, risk assessors should choose appropriate ways to evaluate and characterize epistemic uncertainty. A full treatment of uncertainty requires methods that distinguish aleatory from epistemic uncertainty. Quantitative expressions for epistemic uncertainty are advantageous in scientific assessments because they are nonambiguous and enable individual uncertainties to be characterized and combined in a systematic way. Since 2019, the European Food Safety Authority (EFSA) recommends assessors to express epistemic uncertainty in conclusions of scientific assessments quantitatively by subjective probability. A subjective probability can be used to represent an expert judgment, which may or may not be updated using Bayes's rule to integrate evidence available for the assessment and could be either precise or approximate. Approximate (or bounded) probabilities may be enough for decision making and allow experts to reach agreement on certainty when they struggle to specify precise subjective probabilities. The difference between the lower and upper bound on a subjective probability can also be used to reflect someone's strength of knowledge. In this article, we demonstrate how to quantify uncertainty by bounded probability, and explicitly distinguish between epistemic and aleatory uncertainty, by means of robust Bayesian analysis, including standard Bayesian analysis through precise probability as a special case. For illustration, the two analyses are applied to an intake assessment. [ABSTRACT FROM AUTHOR]

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold beliefs of both types simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List. The nature, relevance, and implications of the tension are explained and assessed.

Consumers routinely rely on forecasters to make predictions about uncertain events (e.g., sporting contests, stock fluctuations). The authors demonstrate that when forecasts are higher versus lower (e.g., a 70% vs. 30% chance of team A winning a game), consumers infer that the forecaster ismore confident in his or her prediction, has conducted more in-depth analyses, and is more trustworthy. Consumers also judge the prediction as more accurate. This occurs because people tend to evaluate forecasts on the basis of how well they predict a target event occurring (e.g., team A winning). Higher forecasts indicate greater likelihood of the target event occurring and signal a confident analyst, while lower forecasts indicate lower likelihood and lower confidence in the target event occurring. Yet because with lower forecasts, consumers still focus on the target event (rather than its complement), lower confidence in the target event occurring is erroneously interpreted as the forecaster being less confident in his or her overall prediction (instead ofmore confident in the complementary event occurring, i.e., team A losing). The authors identify boundary conditions, generalize to other prediction formats, and demonstrate consequences of their findings. [ABSTRACT FROM AUTHOR]

I show that de Finetti's coherence theorem is equivalent to the Hahn-Banach theorem and discuss some consequences of this result. First, the result unites two aspects of de Finetti's thought in a nice way: a corollary of the result is that the coherence theorem implies the existence of a fair countable lottery, which de Finetti appealed to in his arguments against countable additivity. Another corollary of the result is the existence of sets that are not Lebesgue measurable. I offer a subjectivist interpretation of this corollary that is concordant with de Finetti's views. I conclude by pointing out that my result shows that there is a sense in which de Finetti's theory of subjective probability is necessarily nonconstructive. This raises questions about whether the coherence theorem can underwrite a legitimate theory of rational belief. [ABSTRACT FROM AUTHOR]

Bayesian decision analysis is a useful method for risk management decisions, but is limited in its ability to consider severe uncertainty in knowledge, and value ambiguity in management objectives. We study the use of robust Bayesian decision analysis to handle problems where one or both of these issues arise. The robust Bayesian approach models severe uncertainty through bounds on probability distributions, and value ambiguity through bounds on utility functions. To incorporate data, standard Bayesian updating is applied on the entire set of distributions. To elicit our expert's utility representing the value of different management objectives, we use a modified version of the swing weighting procedure that can cope with severe value ambiguity. We demonstrate these methods on an environmental management problem to eradicate an alien invasive marmorkrebs recently discovered in Sweden, which needed a rapid response despite substantial knowledge gaps if the species was still present (i.e., severe uncertainty) and the need for difficult tradeoffs and competing interests (i.e., value ambiguity). We identify that the decision alternatives to drain the system and remove individuals in combination with dredging and sieving with or without a degradable biocide, or increasing pH, are consistently bad under the entire range of probability and utility bounds. This case study shows how robust Bayesian decision analysis provides a transparent methodology for integrating information in risk management problems where little data are available and/or where the tradeoffs are ambiguous. [ABSTRACT FROM AUTHOR]

Due to climatic hazards and extreme weather events, the pricing of property insurance products is increasingly attracting the attention of policyholders, insurance companies, and governments. Pricing based on market-oriented methods has to consider the affecting factors from policyholders' perceived value. Pricing strategy design generates the need for natural hazards risk assessments. A natural hazard risk assessment is closely related to the human factors of a disaster-bearing body. In response to this need, we design an extension of the expected utility that is inconsistent with the additive expected utility, considering the human factors of policyholders, which is referred to as the expected loss utility (ELU). The ELU presents two improvements of the currently used utility. First, subjective probability, which is derived from individual predictions over acts, is applied to the ELU function to overcome the disadvantage that objective probability attaches to uncertainty does not reflect the uncertainty of human factors. Policyholders' risk attitudes are reflected by the interpretation of interactions among uncertain events. Second, the hesitant fuzzy linguistic preference relation (HFLPR) is employed as the assessment of individual loss evaluation to reflect a policyholder's hesitation. We apply the techniques of fuzzy linguistic term aggregation and perform a comparison to simplify our loss utility function. A detailed process of expected loss assessment is proposed due to variations in natural environment factors, local social characteristics, and disaster-bearing body factors. An illustrative example is given to perform a comparison with cumulative prospect theory to show the merits of the ELU. This study quantifies policyholder's cognition of uncertain event and the cognition's influence on risk assessment which can guide pricing strategy of property insurance products. [ABSTRACT FROM AUTHOR]