Search

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 quant

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 quant

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 quant

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 quant

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 quant

Uncertainty refers to any limitation in knowledge. Identifying and characterizing uncertainty in conclusions is important to ensure transparency and avoid over or under confidence in scientific assessments. Quantitative expressions of uncertainty are less ambiguous compared to uncertainty expressed qualitatively, or not at all. Subjective probability is an example of a quantitative expression of epistemic uncertainty, which combined with Bayesian inference makes it possible to integrate evidence and characterizes uncertainty in quantities of interest. This thesis contributes to the understanding and implementation of robust Bayesian analysis as a way to integrate expert judgment and data into assessments and quantify uncertainty by bounded probability. The robust Bayesian framework is based on sets of probability for epistemic uncertainty, where precise probability is seen as a special case. This thesis covers applications relevant for scientific assessments, including evidence synthesis and quantitative risk assessment.Paper I proposes to combine two sampling methods: iterative importance sampling and Markov chain Monte Carlo (MCMC) sampling, for quantifying uncertainty by bounded probability when Bayesian updating requires MCMC sampling. This opens up for robust Bayesian analysis to be applied to complex statistical models. To achieve this, an effective sample size of importance sampling that accounts for correlated MCMC samples is proposed. For illustration, the proposed method is applied to estimate the overall effect with bounded probability in a published meta-analysis within the Collaboration for Environmental Evidence on the effect of biomanipulation on freshwater lakes.Paper II demonstrates robust Bayesian analysis as a way to quantify uncertainty in a quantity of interest by bounded probability, and explicitly distinguishes between epistemic and aleatory uncertainty in the assessment and learn parameters by integrating evidence into the model. Robust Bayes

Consequentialism says that consequences settle what ought to be done. What does this imply for how we should decide, on some given occasion, what ought to be done in the light of our beliefs about the consequences of the actions available to us, our options? We explore the issues generated by the fact that typically there is substantial uncertainty about the consequences of the actions we need to choose between—we perforce must rely on the subjective probabilities of the possible outcomes of those actions. We distinguish objective “oughts” from expective “oughts” and note the complications that arise with compound actions—actions that have actions as parts.

This dissertation concerns the interpretation and structure of two intuitive notions: rational credence and confirmation. Probabilistic accounts of rational credence currently enjoy a position of considerable prestige, underwriting significant work not only in philosophy but also in economics and statistics. Confirmation, in contrast, is widely regarded as ill-formed, a misleading misconception akin to phlogiston, witches, or cosmic ether (de Finetti x). The primary project of this dissertation is to undercut the contemporary consensus on both notions by first demonstrating a systemic weakness in probabilistic accounts of rational credence (part I) and then providing a non-probabilistic account of confirmation (part II). Since any adequate account of confirmation is prima facie an adequate account of rational credence, the negative work of part one dovetails with the positive account offered in part two. Confirmation is no misleading misconception, and rational credences are not probability functions.

This dissertation concerns the interpretation and structure of two intuitive notions: rational credence and confirmation. Probabilistic accounts of rational credence currently enjoy a position of considerable prestige, underwriting significant work not only in philosophy but also in economics and statistics. Confirmation, in contrast, is widely regarded as ill-formed, a misleading misconception akin to phlogiston, witches, or cosmic ether (de Finetti x). The primary project of this dissertation is to undercut the contemporary consensus on both notions by first demonstrating a systemic weakness in probabilistic accounts of rational credence (part I) and then providing a non-probabilistic account of confirmation (part II). Since any adequate account of confirmation is prima facie an adequate account of rational credence, the negative work of part one dovetails with the positive account offered in part two. Confirmation is no misleading misconception, and rational credences are not probability functions.

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.

Under state-dependent preferences, probabilities and units of scale of state-dependent utilities are not separately identified, in standard models: only their products matter to decisions. Separate identification has been studied under implicit actions (Drèze 1961,1987) or under explicit actions and observations (Karni 2011, 2013). This paper complements both approaches and relates them, them, when conditional preferences for final outcomes are independent of actions and observations. That special case permits drastic technical simplification while remaining open to some natural extensions

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.

This thesis consists of an introductory part and four self-contained papers related to individual investors’ subjective expectations and their financial behavior. Paper [I] analyzes multiple measures of individual investors’ expectations of risk and return using survey data on a random sample of individual investors in Sweden. The results indicate that, even though expectations from different measures are correlated, the magnitude of especially the risk expectations varies considerably between measures. The variations in the expectations mainly relate to differences in the responses to the questions underlying the different measures, rather than to the methods used to obtain them. Evaluation of the measures using three different comparisons indicates that the expectation measure proposed by Dominitz and Manski (2011) is the only measure for which it is possible to distinguish between individuals’ expectations using all of the considered comparisons. Paper [II] addresses the relationship between sophistication and the expectations of individual investors with respect to risk and return. The findings show that sophisticated investors have lower (higher) risk (return) expectations that are closer to objective measures than less sophisticated investors. These results are important, since they enhance the understanding of the underlying mechanisms through which sophistication could influence individuals’ financial decisions. Paper [III] provides new evidence for the sources of information individual investors’ use when making financial decisions and the relationship between how frequently investors use this information and their expectations of the risk and return in a stock market index, their confidence in these expectations, and their portfolio risk and return. The findings indicate that individual investors use different sources of filtered financial information (e.g., information packaged by a professional intermediary) more frequently than unfiltered financial inf

This thesis consists of an introductory part and four self-contained papers related to individual investors’ subjective expectations and their financial behavior. Paper [I] analyzes multiple measures of individual investors’ expectations of risk and return using survey data on a random sample of individual investors in Sweden. The results indicate that, even though expectations from different measures are correlated, the magnitude of especially the risk expectations varies considerably between measures. The variations in the expectations mainly relate to differences in the responses to the questions underlying the different measures, rather than to the methods used to obtain them. Evaluation of the measures using three different comparisons indicates that the expectation measure proposed by Dominitz and Manski (2011) is the only measure for which it is possible to distinguish between individuals’ expectations using all of the considered comparisons. Paper [II] addresses the relationship between sophistication and the expectations of individual investors with respect to risk and return. The findings show that sophisticated investors have lower (higher) risk (return) expectations that are closer to objective measures than less sophisticated investors. These results are important, since they enhance the understanding of the underlying mechanisms through which sophistication could influence individuals’ financial decisions. Paper [III] provides new evidence for the sources of information individual investors’ use when making financial decisions and the relationship between how frequently investors use this information and their expectations of the risk and return in a stock market index, their confidence in these expectations, and their portfolio risk and return. The findings indicate that individual investors use different sources of filtered financial information (e.g., information packaged by a professional intermediary) more frequently than unfiltered financial inf

Purpose The purpose of this paper is to measure individual investors’ expectations of risk and return and to evaluate different expectation measures. Design/methodology/approach The authors measure individual investors’ expectations of risk and return regarding an index fund and two stocks using survey data on a random sample of individual investors in Sweden. The survey contains three different return and four different risk expectation measures. To evaluate the different expectation measures, three different evaluation perspectives are considered. Findings The risk expectations obtained from the different measures are positively correlated across respondents, but their average magnitudes differ considerably across measures. The return expectations are also positively correlated, and their magnitudes also differ, but to a lesser extent. Consequently, the same individual can express risk expectations that either underestimate or overestimate the forward risk, depending on the measure that is used. The variations in the expectations mainly relate to differences in the responses to the questions underlying the different measures, rather than to the methods used to obtain the expectations. The results from the evaluation of the measures indicate that the expectation measure proposed by Dominitz and Manski (2011) is the only measure for which it is possible to distinguish between individuals’ expectations, using all three of the evaluation perspectives. Originality/value This is, to the best of the authors’ knowledge, the first paper that evaluates different survey measures of individual investors’ expectations of risk and return.

The purpose with this study is to show how the subjective uncertainty analysis can be applied to the cost estimates and examine how the attitudes towards risk budgeting of construction projects works. Biogas Mellannorrland is based on a case study and focuses on four location options for the biogas plant. For each option, a cost estimate in form of a fixed cost and variable cost elements, where the latter are uncertain. Pearson-Tukey method have been applied as a method to estimating subjective probabilities. An assumption is made so that the uncertain costs are normally distributed, where the parameters’ mean and standard deviation collected from respondents indicating percentiles at 5% and 95% for doubtful cost elements. In order to identify the project managers risk attitude, the risk premium method will be used to calculate where the expected value is produced by Pearson-Tukey method. The expected value is subtracted with certainty equivalent, which consist of the budgeted amount. The study was conducted through interviews in order to obtain the costs and the subjective probabilities. The study results show that it is difficult to determine which option is the best, or the worst, by just looking at the expected value. The risk premium shows that each option is a risk averse choice for the project managers, since the risk premium was greater than zero., Denna studie syftar till att visa hur subjektiv osäkerhetsanalys kan tillämpas vid kostnadskalkyler samt undersöka riskattityder vid budgetering av byggprojekt. Undersökningen är en fallstudie vid Biogas Mellannorrland och fokuserar på fyra lokaliseringsalternativ för biogasanläggning. För varje alternativ görs en kostnadskalkyl i form av ett antal fasta och rörliga delkostnader, där de senare är osäkra. Som metod för att skatta subjektiva sannolikheter har Pearson-Tukey-metoden tillämpats. Ett antagande görs att osäkra kostnader är normalfördelade, där parametrarna väntevärde och standardavvikelse hämtas från respondenter som anger percentilerna vid 5 % och 95 % för osäkra delkostnader. För att identifiera projektledarnas riskattityd, kommer riskpremium att beräknas, där det förväntade värdet tas fram med Pearson-Tukey- metoden. Det förväntade värdet subtraheras med säkerhetsekvivalensen, vilket utgörs av det budgeterade beloppet. Studien har genomförts med hjälp av intervjuer för att få fram kostnader och subjektiva sannolikheter. Studiens resultat visar att det är svårt att avgöra vilka alternativ som är bäst eller sämst genom att bara titta på väntevärdet. Med riskpremium visar alla alternativ att projektledarna gör ett riskaversivt val, eftersom riskpremium blev större än noll.

The purpose with this study is to show how the subjective uncertainty analysis can be applied to the cost estimates and examine how the attitudes towards risk budgeting of construction projects works. Biogas Mellannorrland is based on a case study and focuses on four location options for the biogas plant. For each option, a cost estimate in form of a fixed cost and variable cost elements, where the latter are uncertain. Pearson-Tukey method have been applied as a method to estimating subjective probabilities. An assumption is made so that the uncertain costs are normally distributed, where the parameters’ mean and standard deviation collected from respondents indicating percentiles at 5% and 95% for doubtful cost elements. In order to identify the project managers risk attitude, the risk premium method will be used to calculate where the expected value is produced by Pearson-Tukey method. The expected value is subtracted with certainty equivalent, which consist of the budgeted amount. The study was conducted through interviews in order to obtain the costs and the subjective probabilities. The study results show that it is difficult to determine which option is the best, or the worst, by just looking at the expected value. The risk premium shows that each option is a risk averse choice for the project managers, since the risk premium was greater than zero., Denna studie syftar till att visa hur subjektiv osäkerhetsanalys kan tillämpas vid kostnadskalkyler samt undersöka riskattityder vid budgetering av byggprojekt. Undersökningen är en fallstudie vid Biogas Mellannorrland och fokuserar på fyra lokaliseringsalternativ för biogasanläggning. För varje alternativ görs en kostnadskalkyl i form av ett antal fasta och rörliga delkostnader, där de senare är osäkra. Som metod för att skatta subjektiva sannolikheter har Pearson-Tukey-metoden tillämpats. Ett antagande görs att osäkra kostnader är normalfördelade, där parametrarna väntevärde och standardavvikelse hämtas från respondenter som anger percentilerna vid 5 % och 95 % för osäkra delkostnader. För att identifiera projektledarnas riskattityd, kommer riskpremium att beräknas, där det förväntade värdet tas fram med Pearson-Tukey- metoden. Det förväntade värdet subtraheras med säkerhetsekvivalensen, vilket utgörs av det budgeterade beloppet. Studien har genomförts med hjälp av intervjuer för att få fram kostnader och subjektiva sannolikheter. Studiens resultat visar att det är svårt att avgöra vilka alternativ som är bäst eller sämst genom att bara titta på väntevärdet. Med riskpremium visar alla alternativ att projektledarna gör ett riskaversivt val, eftersom riskpremium blev större än noll.

In this response paper, part of the Virtual Special Issue on “Measuring and Reporting the Precision of Forensic Likelihood Ratios”, we further develop our position on likelihood ratios which we described previously in Berger et al. (2016) “The LR does not exist”. Our exposition is inspired by an example given in Martire et al. (2016) “On the likelihood of encapsulating all uncertainty”, where the consequences of obtaining additional information on the LR were discussed. In their example, two experts use the same data in a different way, and the LRs of these experts change differently when new data are taken into account. Using this example as a starting point we will demonstrate that the probability distribution for the frequency of the characteristic observed in trace and reference material can be used to predict how much an LR will change when new data become available. This distribution can thus be useful for such a sensitivity analysis, and address the question of whether to obtain additional data or not. But it does not change the answer to the original question of how to update one's prior odds based on the evidence, and it does not represent an uncertainty on the likelihood ratio based on the current data.

This thesis consists of an introductory part and four self-contained papers related to individual investors’ subjective expectations and their financial behavior. Paper [I] analyzes multiple measures of individual investors’ expectations of risk and return using survey data on a random sample of individual investors in Sweden. The results indicate that, even though expectations from different measures are correlated, the magnitude of especially the risk expectations varies considerably between measures. The variations in the expectations mainly relate to differences in the responses to the questions underlying the different measures, rather than to the methods used to obtain them. Evaluation of the measures using three different comparisons indicates that the expectation measure proposed by Dominitz and Manski (2011) is the only measure for which it is possible to distinguish between individuals’ expectations using all of the considered comparisons. Paper [II] addresses the relationship between sophistication and the expectations of individual investors with respect to risk and return. The findings show that sophisticated investors have lower (higher) risk (return) expectations that are closer to objective measures than less sophisticated investors. These results are important, since they enhance the understanding of the underlying mechanisms through which sophistication could influence individuals’ financial decisions. Paper [III] provides new evidence for the sources of information individual investors’ use when making financial decisions and the relationship between how frequently investors use this information and their expectations of the risk and return in a stock market index, their confidence in these expectations, and their portfolio risk and return. The findings indicate that individual investors use different sources of filtered financial information (e.g., information packaged by a professional intermediary) more frequently than unfiltered financial inf

This thesis consists of an introductory part and four self-contained papers related to individual investors’ subjective expectations and their financial behavior. Paper [I] analyzes multiple measures of individual investors’ expectations of risk and return using survey data on a random sample of individual investors in Sweden. The results indicate that, even though expectations from different measures are correlated, the magnitude of especially the risk expectations varies considerably between measures. The variations in the expectations mainly relate to differences in the responses to the questions underlying the different measures, rather than to the methods used to obtain them. Evaluation of the measures using three different comparisons indicates that the expectation measure proposed by Dominitz and Manski (2011) is the only measure for which it is possible to distinguish between individuals’ expectations using all of the considered comparisons. Paper [II] addresses the relationship between sophistication and the expectations of individual investors with respect to risk and return. The findings show that sophisticated investors have lower (higher) risk (return) expectations that are closer to objective measures than less sophisticated investors. These results are important, since they enhance the understanding of the underlying mechanisms through which sophistication could influence individuals’ financial decisions. Paper [III] provides new evidence for the sources of information individual investors’ use when making financial decisions and the relationship between how frequently investors use this information and their expectations of the risk and return in a stock market index, their confidence in these expectations, and their portfolio risk and return. The findings indicate that individual investors use different sources of filtered financial information (e.g., information packaged by a professional intermediary) more frequently than unfiltered financial inf

This thesis consists of an introductory part and four self-contained papers related to individual investors’ subjective expectations and their financial behavior. Paper [I] analyzes multiple measures of individual investors’ expectations of risk and return using survey data on a random sample of individual investors in Sweden. The results indicate that, even though expectations from different measures are correlated, the magnitude of especially the risk expectations varies considerably between measures. The variations in the expectations mainly relate to differences in the responses to the questions underlying the different measures, rather than to the methods used to obtain them. Evaluation of the measures using three different comparisons indicates that the expectation measure proposed by Dominitz and Manski (2011) is the only measure for which it is possible to distinguish between individuals’ expectations using all of the considered comparisons. Paper [II] addresses the relationship between sophistication and the expectations of individual investors with respect to risk and return. The findings show that sophisticated investors have lower (higher) risk (return) expectations that are closer to objective measures than less sophisticated investors. These results are important, since they enhance the understanding of the underlying mechanisms through which sophistication could influence individuals’ financial decisions. Paper [III] provides new evidence for the sources of information individual investors’ use when making financial decisions and the relationship between how frequently investors use this information and their expectations of the risk and return in a stock market index, their confidence in these expectations, and their portfolio risk and return. The findings indicate that individual investors use different sources of filtered financial information (e.g., information packaged by a professional intermediary) more frequently than unfiltered financial inf

This paper proposes a formal characterization of extended Bayesian updating for complementarily additive subjective beliefs under ambiguity, which are compatible with a wide range of choice behavior toward ambiguity. The main result shows that, based on the biseparability of Ghirardato and Marinacci (2001), extended Bayesian updating characterizes the update rule which is a step-by-step composite updating for priors, where one of Dempster-Shafer rule, Bayes'update rule and Fagin-Halpern rule is applied to each step. As applications, more speci c preference relations are examined, such as the maxmin expected utility, the rank-dependent expected utility, and the concave expected utility preferences by Lehrer (2009).

We examine how people judge the probabilities of real-world events, such as natural disasters in different countries. We find that the associations between the words and phrases that constitute these events, as assessed by vector space semantic models, strongly correlate with the probabilities assigned to these events by participants. Thus, for example, the semantic proximity of “earthquake” and “Japan” accurately predicts judgments regarding the probability of an earthquake in Japan. Our results suggest that the mechanisms and representations at play in language are also active in high- level domains, such as judgment and decision making, and that existing insights regarding these representations can be used to make precise, quantitative, a priori predictions regarding the probability estimates of individuals.

This article revises the popular issue of collinearity amongst explanatory variables in the context of a multiple linear regression analysis, particularly in empirical studies within social science related fields. Some important interpretations and explanations are highlighted from the econometrics literature with respect to the effects of multicollinearity on statistical inference, as well as the general shortcomings of the once fervent search for methods intended to detect and mitigate these effects. Consequently, it is argued and demonstrated through simulation how these views may be resolved against an alternative methodology by integrating a researcher’s subjective information in a formal and systematic way through a Bayesian approach.

We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability-one the basic laws of classical probability theory.

Little is known about perceptions of medical expenditure risks despite their presumed relevance to health insurance demand. This paper reports on a unique elicitation of subjective probabilities of medical expenditures from rural Ethiopians who are offered the opportunity to purchase health insurance. We find that expectations are positively correlated with past expenses to a degree that exceeds the serial correlation in realized expenditures, suggesting overestimation of persistence and underestimation of the potential gains from insurance. Despite the fact that forecast expenditures do predict realized expenditures to some extent, there is no evidence that expectations influence the decision to take out health insurance, although plans to insure are positively related to the percei

Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an (operational) interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework generalises the classical Dutch Book method. © 2015 Elsevier Inc.

Current supervaluation models of opinion, notably van Fraassen's (1984; 1989; 1990; 1998; 2005; 2006) use of intervals to characterize vague opinion, capture nuances of ordinary reflection which are overlooked by classic measure theoretic models of subjective probability. However, after briefly explaining van Fraassen's approach, we present two limitations in his current framework which provide clear empirical reasons for seeking a refinement. Any empirically adequate account of our actual judgments must reckon with the fact that these are typically neither uniform through the range of outcomes we take to be serious possibilities nor abrupt at the edges.

In the previous chapter we measured the quality of an investment in terms of the expected value E[V1] and the variance Var(V1) of the future portfolio value V1 and determined portfolio weights (subject to constraints) that maximize a suitable trade-off$$\mathrm{E}[{V }_{1}] - c\mathrm{Var}({V }_{1})/(2{V }_{0})$$ between a large expected value and a small variance. Attractive features of this approach are that the probability distribution of V1 does not have to be specified in detail and that explicit expressions for the optimal portfolio weights are found that have intuitive interpretations. We saw that this approach makes perfect sense if we consider portfolio values V1 that can be expressed as linear combinations of asset returns whose joint distribution is a multivariate normal distribution. However, unless there are good reasons to assume a multivariate normal distribution (or, more generally, as will be made clear in Chap. 9, an elliptical distribution), solutions provided by the quadratic investment principles can be rather misleading. Here we want to allow for a probability distribution of any kind, and this calls for more general investment principles that are not only based on the variance and expected value of V1., QC 20210413

Current supervaluation models of opinion, notably van Fraassen's (1984; 1989; 1990; 1998; 2005; 2006) use of intervals to characterize vague opinion, capture nuances of ordinary reflection which are overlooked by classic measure theoretic models of subjective probability. However, after briefly explaining van Fraassen's approach, we present two limitations in his current framework which provide clear empirical reasons for seeking a refinement. Any empirically adequate account of our actual judgments must reckon with the fact that these are typically neither uniform through the range of outcomes we take to be serious possibilities nor abrupt at the edges.

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance.

In 2010, the US Intelligence Advanced Research Projects Activity (IARPA) announced a 4-year forecasting “tournament”. Five collaborative research teams are attempting to outperform a baseline opinion pool in predicting hundreds of geopolitical, economic and military events. We are contributing to one of these teams by eliciting forecasts from Delphi-style groups in the US and Australia. We elicit probabilities of outcomes for 3-5 monthly questions, such as: Will Australia formally transfer uranium to India by 1 June 2012? Participants submit probabilities in a 3-step interval format, view those of others in their group, share, rate and discuss information, and then make a second private judgement. Performance is assessed using Brier scores. After Year 1, we ranked second of five teams in the competition. The Brier scores from the US Delphi groups improved on the baseline scores by 10%, the prediction market operated by our team in the US beat the baseline by 47%, and the Australian Delphi groups outperformed the baseline by 51% (answering different, matched questions to the US groups). The Australian groups were more socially and demographically diverse than the US groups. Group diversity may be an important factor determining the forecasting performance of the aggregated predictions.

In survey studies, probabilistic expectations about uncertain events are typically elicited by asking respondents for their introspective beliefs. If more complex procedures are feasible, beliefs can be elicited by incentive compatible revealed preference mechanisms (“truth serums”). Various mechanisms have been proposed in the literature, which differ in the degree to which they account for respondents’ deviations from expected value maximization. In this paper, we pit non-incentivized introspection against five truth serums, to elicit beliefs in a simple two-player game. We test the internal validity (additivity and predictive power for own behavior), and the external validity (predictive power for other players’ behavior, or accuracy) of each method. We find no differences among the truth serums. Beliefs from incentivized methods are better predictors of subjects’ own behavior compared to introspection. However, introspection performs equally well as the truth serums in terms of accuracy and additivity.

In economic decisions we often have to deal with uncertain events for which no probabilities are known. Several normative models have been proposed for such decisions. Empirical studies have usually been qualitative, or they estimated ambiguity aversion through one single number. This paper introduces the source method, a tractable method for quantitatively analyzing uncertainty empirically that can capture the richness of ambiguity attitudes. The theoretical key in our method is the distinction between different sources of uncertainty, within which subjective (choice-based) probabilities can still be defined. Source functions convert those subjective probabilities into willingness to bet. We apply our method in an experiment, where we do not commit to particular ambiguity attitudes but let the data speak.

Two types of measures of probabilistic uncertainty are introduced and investigated. Dispersion measures report how diffused the agent's second-order probability distribution is over the range of first-order probabilities. Robustness measures reflect the extent to which the agent's assessment of the prior (objective) probability of an event is perturbed by information about whether or not the event actually took place. The properties of both types of measures are investigated. The most obvious type of robustness measure is shown to coincide with one of the major candidates for a dispersion measure, the mean square deviation measure., QC 20120216

When confronted with uncertain prospects, people often exhibit both choice deferral and Ellsberg-type ambiguity aversion. This paper obtains a joint representation for these behavioral phenomena. The decision maker as portrayed by my model is willing to choose an uncertain prospect f over g rather than to defer this choice if and only if the expected utility of f is greater that or equal to the expected utility of g for every probability measure in a convex and closed set Delta. This set is interpreted as a collection of the decision maker's possible future beliefs. When choices cannot be deferred, the decision maker evaluates every uncertain prospect via an epsilon-mixture of the least favorable element in the set Delta and her current probabilistic belief p is an element of Delta. All components of my model are derived from observable preferences in an essentially unique way.

When confronted with uncertain prospects, people often exhibit both choice deferral and Ellsberg-type ambiguity aversion. This paper obtains a joint representation for these behavioral phenomena. The decision maker as portrayed by my model is willing to choose an uncertain prospect f over g rather than to defer this choice if and only if the expected utility of f is greater that or equal to the expected utility of g for every probability measure in a convex and closed set Delta. This set is interpreted as a collection of the decision maker's possible future beliefs. When choices cannot be deferred, the decision maker evaluates every uncertain prospect via an epsilon-mixture of the least favorable element in the set Delta and her current probabilistic belief p is an element of Delta. All components of my model are derived from observable preferences in an essentially unique way.

The idea that people often make probability judgments by a heuristic short-cut, the representativeness heuristic, has been widely influential, but also criticized for being vague. The empirical trademark of the heuristic is characteristic deviations between normative probabilities and judgments (e.g., the conjunction fallacy, base-rate neglect). In this article the authors contrast two hypotheses concerning the cognitive substrate of the representativeness heuristic, the prototype hypothesis (Kahneman & Frederick, 2002) and the exemplar hypothesis (Juslin & Persson, 2002), in a task especially designed to elicit representativeness effects. Computational modelling and an experiment reveal that representativeness effects are evident early in training and persist longer in a more complex task environment and that the data are best accounted for by a model implementing the exemplar hypothesis.

Research with general knowledge items demonstrates extreme overconfidence when people estimate confidence intervals for unknown quantities, but close to zero overconfidence when the same intervals are assessed by probability judgment. In 3 experiments, the authors investigated if the overconfidence specific to confidence intervals derives from limited task experience or from short-term memory limitations. As predicted by the naive sampling model (P. Juslin, A. Winman, & P. Hansson, 2007), overconfidence with probability judgment is rapidly reduced by additional task experience, whereas overconfidence with intuitive confidence intervals is minimally affected even by extensive task experience. In contrast to the minor bias with probability judgment, the extreme overconfidence bias with intuitive confidence intervals is correlated with short-term memory capacity. The proposed interpretation is that increased task experience is not sufficient to cure the overconfidence with confidence intervals because it stems from short-term memory limitations.

The literature presents two major theories on the cause of the conjunction fallacy. The first attributes the conjunction fallacy to the representativeness heuristic. The second suggests that the conjunction fallacy is caused by people combining p(A) and p(B) into p(A&B) in an inappropriate manner. These two theories were contrasted in two category-learning experiments. As predicted by the latter theory, data showed that participants that could assess p(A&B) directly made fewer conjunction fallacies than participants who had to compute p(A) and p(B) separately and then combine them into p(A&B). Least conjunction fallacies were observed in the cases where the representativeness heuristic was applicable. Overall, data showed that an inability to appropriately combine probabilities is one of the key cognitive mechanisms behind the conjunction fallacy.

According to the heuristics and biases approach, the representativeness heuristic (RH) is one of the heuristics available for assessing subjective probabilities (A. Tversky & D. Kahneman, 1974). A subjective probability assessed by the RH is determined by how representative the target object is of the target category. Several aspects of the RH are argued to cause systematic biases, for example: (i) When the RH is used, the category is represented by one single prototypical exemplar. This feature is argued to cause biases such as misperception of chance and insensitivity to sample size. (ii) The RH assesses the inverse rather than the conditional probability. This feature is argued to cause biases such as the conjunction fallacy and base-rate neglect. The present thesis focuses on the cognitive aspects of the RH. Three studies were conducted. Overall, data indicated that the RH does not play a major role when subjective probabilities are assessed. Study I indicated that subjective probabilities are not typically determined by how representative the target object is of the target category. Study II indicated that the category is not represented by one single prototypical exemplar when subjective probabilities are assessed. Study III indicated that conjunction fallacies are not caused by the RH. The results presented in Studies I-III cast serious doubts on the claim that subjective probabilities are routinely assessed using the RH. Rather, Studies I-II suggested that subjective probabilities are based on exemplar memory and Study III suggested that the conjunction fallacy is caused by people combining component probabilities in a an inappropriate way. In the General Discussion, it is suggested that people use a weighted average rule when combining component probabilities into conjunction probabilities. A simulation showing the ecological relevance of the weighted average rule is presented.

According to the heuristics and biases approach, the representativeness heuristic (RH) is one of the heuristics available for assessing subjective probabilities (A. Tversky & D. Kahneman, 1974). A subjective probability assessed by the RH is determined by how representative the target object is of the target category. Several aspects of the RH are argued to cause systematic biases, for example: (i) When the RH is used, the category is represented by one single prototypical exemplar. This feature is argued to cause biases such as misperception of chance and insensitivity to sample size. (ii) The RH assesses the inverse rather than the conditional probability. This feature is argued to cause biases such as the conjunction fallacy and base-rate neglect. The present thesis focuses on the cognitive aspects of the RH. Three studies were conducted. Overall, data indicated that the RH does not play a major role when subjective probabilities are assessed. Study I indicated that subjective probabilities are not typically determined by how representative the target object is of the target category. Study II indicated that the category is not represented by one single prototypical exemplar when subjective probabilities are assessed. Study III indicated that conjunction fallacies are not caused by the RH. The results presented in Studies I-III cast serious doubts on the claim that subjective probabilities are routinely assessed using the RH. Rather, Studies I-II suggested that subjective probabilities are based on exemplar memory and Study III suggested that the conjunction fallacy is caused by people combining component probabilities in a an inappropriate way. In the General Discussion, it is suggested that people use a weighted average rule when combining component probabilities into conjunction probabilities. A simulation showing the ecological relevance of the weighted average rule is presented.

Based on the setting of exchangeable bets, this paper proposes a subjectivist view of numerical possibility theory. It relies on the assumption that when an agent constructs a probability measure by assigning prices to lotteries, this probability measure is actually induced by a belief function representing the agent's actual state of knowledge. We also assume that the probability measure proposed by the agent in the course of the elicitation procedure is constructed via the so-called pignistic transformation (mathematically equivalent to the Shapley value in game theory). We pose and solve the problem of finding the least informative belief function having a given pignistic probability. We prove that it is unique and consonant, thus induced by a possibility distribution. This result exploits a simple informational ordering, in agreement with partial orderings between belief functions, comparing their information content. The obtained possibility distribution is subjective in the same sense as in the subjectivist school in probability theory. However, we claim that it is the least biased representation of the agent's state of knowledge compatible with the observed betting behaviour. © 2007 Elsevier Inc. All rights reserved., SCOPUS: ar.j, info:eu-repo/semantics/published

According to the heuristics and biases approach, the representativeness heuristic (RH) is one of the heuristics available for assessing subjective probabilities (A. Tversky & D. Kahneman, 1974). A subjective probability assessed by the RH is determined by how representative the target object is of the target category. Several aspects of the RH are argued to cause systematic biases, for example: (i) When the RH is used, the category is represented by one single prototypical exemplar. This feature is argued to cause biases such as misperception of chance and insensitivity to sample size. (ii) The RH assesses the inverse rather than the conditional probability. This feature is argued to cause biases such as the conjunction fallacy and base-rate neglect. The present thesis focuses on the cognitive aspects of the RH. Three studies were conducted. Overall, data indicated that the RH does not play a major role when subjective probabilities are assessed. Study I indicated that subjective probabilities are not typically determined by how representative the target object is of the target category. Study II indicated that the category is not represented by one single prototypical exemplar when subjective probabilities are assessed. Study III indicated that conjunction fallacies are not caused by the RH. The results presented in Studies I-III cast serious doubts on the claim that subjective probabilities are routinely assessed using the RH. Rather, Studies I-II suggested that subjective probabilities are based on exemplar memory and Study III suggested that the conjunction fallacy is caused by people combining component probabilities in a an inappropriate way. In the General Discussion, it is suggested that people use a weighted average rule when combining component probabilities into conjunction probabilities. A simulation showing the ecological relevance of the weighted average rule is presented.

Based on the setting of exchangeable bets, this paper proposes a subjectivist view of numerical possibility theory. It relies on the assumption that when an agent constructs a probability measure by assigning prices to lotteries, this probability measure is actually induced by a belief function representing the agent's actual state of knowledge. We also assume that the probability measure proposed by the agent in the course of the elicitation procedure is constructed via the so-called pignistic transformation (mathematically equivalent to the Shapley value in game theory). We pose and solve the problem of finding the least informative belief function having a given pignistic probability. We prove that it is unique and consonant, thus induced by a possibility distribution. This result exploits a simple informational ordering, in agreement with partial orderings between belief functions, comparing their information content. The obtained possibility distribution is subjective in the same sense as in the subjectivist school in probability theory. However, we claim that it is the least biased representation of the agent's state of knowledge compatible with the observed betting behaviour. © 2007 Elsevier Inc. All rights reserved., SCOPUS: ar.j, info:eu-repo/semantics/published

According to the heuristics and biases approach, the representativeness heuristic (RH) is one of the heuristics available for assessing subjective probabilities (A. Tversky & D. Kahneman, 1974). A subjective probability assessed by the RH is determined by how representative the target object is of the target category. Several aspects of the RH are argued to cause systematic biases, for example: (i) When the RH is used, the category is represented by one single prototypical exemplar. This feature is argued to cause biases such as misperception of chance and insensitivity to sample size. (ii) The RH assesses the inverse rather than the conditional probability. This feature is argued to cause biases such as the conjunction fallacy and base-rate neglect. The present thesis focuses on the cognitive aspects of the RH. Three studies were conducted. Overall, data indicated that the RH does not play a major role when subjective probabilities are assessed. Study I indicated that subjective probabilities are not typically determined by how representative the target object is of the target category. Study II indicated that the category is not represented by one single prototypical exemplar when subjective probabilities are assessed. Study III indicated that conjunction fallacies are not caused by the RH. The results presented in Studies I-III cast serious doubts on the claim that subjective probabilities are routinely assessed using the RH. Rather, Studies I-II suggested that subjective probabilities are based on exemplar memory and Study III suggested that the conjunction fallacy is caused by people combining component probabilities in a an inappropriate way. In the General Discussion, it is suggested that people use a weighted average rule when combining component probabilities into conjunction probabilities. A simulation showing the ecological relevance of the weighted average rule is presented.