Decision making under risk and uncertainty

The purpose of this research is to seek the best (highest performing) risk profiles of agents who successively choose among risky prospects. An agent'sr isk profile is his attitude to perceived risk, which can vary from risk preferring to risk neutral (an expected-value decision maker) to risk averse, or even a dual-risk attitude. Weu se the Genetic Algorithm to search in the complex stochastic space of repeated lotteries. We examine three families of utility (or value) functions: wealth-independent CARA and wealth-dependent CRRA, in which an agent'sr isk profile is unchanging, and the Dual-Risk Profile (DRP) function from Prospect Theory,i nw hich the agent can be risk averse (for gains) or risk preferring (for losses). Analysis of the simulation results reveals that the best function for risky decision-making is the risk-neutral linear function.

There is a large volume of research showing that emotions have relevant effects on decision-making. We contribute to this literature by experimentally investigating the impact of four specific emotional states – joviality, sadness, fear, and anger – on risk attitudes. In order to do so, we fit two models of behavior under risk: the Expected Utility model (EU) and the Rank Dependent Expected Utility model (RDEU), assuming several functional forms of the weighting function. Our results indicate that all emotional states mitigate risk aversion. Furthermore, we show that there are some differences across gender and participants' experience in laboratory experiments.

Evidence theory, also called belief function theory, provides an efficient tool to represent and combine uncertain information for pattern classification. Evidence combination can be interpreted, in some applications, as classifier fusion. The sources of evidence corresponding to multiple classifiers usually exhibit different classification qualities, and they are often discounted using different weights before combination. In order to achieve the best possible fusion performance, a new credal belief redistribution (CBR) method is proposed to revise such evidence. The rationale of CBR consists of transferring belief from one class not just to other classes, but also to the associated disjunctions of classes (i.e., meta-classes). As classification accuracy for different objects in a given classifier can also vary, the evidence is revised according to prior knowledge mined from its training neighbors. If the selected neighbors are relatively close to the evidence, a large amount of
belief will be discounted for redistribution. Otherwise, only a small
fraction of belief will enter the redistribution procedure. An imprecision
matrix estimated based on these neighbors is employed to specifically redistribute the discounted beliefs. This matrix expresses the likelihood of misclassification (i.e., the probability of a test pattern belonging to a class different from the one assigned to it by the classifier). InCBR, the discounted beliefs are divided into two parts. One part is transferred between singleton classes, whereas the other is cautiously committed to the associated meta-classes. By doing this, one can efficiently reduce the chance of misclassification by modeling partial imprecision. The multiple revised pieces of evidence are finally combined by the Dempster–Shafer rule to reduce uncertainty and further improve classification accuracy. The effectiveness of CBR is extensively  validated on several real datasets from the UCI repository and critically compared with that of other related fusion methods.

In this paper we show that three conditions due to Pattanaik when satisfied by a given profile of state-dependent preferences (linear orders) on a given and fixed set of alternatives and a probability distribution with which the various states of nature occur are individually sufficient, for the non-emptiness of the set of alternatives alternative(s) which are individually preferred to all alternatives other than itself with probability at least half. Prior to this we show that since each axiom individually implies Sen-Coherence, as a consequence of a result obtained earlier, each axiom along with asymmetry of the “preferred with at probability at least half” relation implies the transitivity of the relation.

RESUMEN Este trabajo analiza la correlación entre las variaciones en el ingreso laboral que consideramos como el capital humano 1 , y el rendimiento del mercado de acciones en la Argentina, para determinar si en este mercado se cumplen los supuestos de independencia entre estas dos variables, tal como lo predicen los trabajos empíricos realizados a la fecha, para el proceso de selección óptima del portafolios de inversores individuales. Para ello se ha tomado el rendimiento del índice MERVAL para representar el rendimiento del mercado de acciones en la Argentina, por un lado, y el nivel de desempleo para representar las variaciones en el nivel del ingreso laboral que consideramos como capital humano, por el otro. Este último se ha desagregado según la edad, el género y el nivel educativo de las personas. Como se demostrará, en un país pequeño con un mercado de capitales pequeño y ciclos macroeconómicos relativamente cortos como sucede en Argentina, existe una considerable correlación entre el rendimiento de las acciones y la tasa de desempleo, haciendo que el capital humano pase a ser un activo riesgoso más junto con las acciones, para ser combinado con el activo libre de riesgo. Esto implicaría que la proporción invertida en acciones para aquellos que tienen un elevado porcentaje de su riqueza en capital humano, debería ser menor que la proporción correspondiente de inversores ubicados en países desarrollados, donde no se detecta la correlación entre las mencionadas variables. JEL Classification: D12; D31; D81; G11

We reexamine some of the classic problems connected with the use of cardinal utility
functions in decision theory, and discuss Patrick Suppes’ contributions to this
field in light of a reinterpretation we propose for these problems. We analytically
decompose the doctrine of ordinalism, which only accepts ordinal utility functions,
and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes’ doctrine with the
major deviation from ordinalism that conceives of utility functions as representing
preference differences, while being nonetheless empirically related to choices. We
highlight the originality, promises and limits of this choice-based cardinalism.

We prove the existence of an expected utility function for preferences over probabilistic prospects satisfying Strict Monotonicity, Indifference, the Common Ration Property, Substitution and Reducibility of Extreme Prospects. The example in Rubinstein (1988) 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 second 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.

In this paper, I examine the decision-theoretic status of risk attitudes. I start by providing evidence showing that the risk attitude concepts do not play a major role in the axiomatic analysis of the classic models of decision-making under risk. This can be interpreted as reflecting the neutrality of these models between the possible risk attitudes. My central claim, however, is that such neutrality needs to be qualified and the axiomatic relevance of risk attitudes needs to be re-evaluated accordingly. Specifically, I highlight the importance of the conditional variation and the strengthening of risk attitudes, and I explain why they establish the axiomatic significance of the risk attitude concepts. I also present several questions for future research regarding the strengthening of risk attitudes.

Background. Numeracy skills are important for medical decision making as lower numeracy is associated with misinterpreting statistical health risks. Math anxiety, characterized by negative emotions about numerical tasks, and lower subjective numeracy (i.e., self-assessments of numerical competence) are also associated with poor risk comprehension. Objective. To explore independent and mediated associations of math anxiety, numerical ability, and subjective numeracy with risk comprehension and to ascertain whether their associations are specific to the health domain. Methods. Objective numeracy was measured with a 14-item test. Math anxiety and subjective numeracy were assessed with self-report scales. Risk comprehension was measured with a 12-item test. In experiment 1, risk comprehension items were limited to scenarios in the health domain. In experiment 2, participants were randomly assigned to receive numerically equivalent risk comprehension items in either a health or nonhealth domain. Results. Linear regression analyses revealed that individuals with higher objective numeracy were more likely to respond correctly to the risk comprehension items, as were individuals with higher subjective numeracy. Higher math anxiety was associated with a lower likelihood of correct responding when controlling for objective numeracy but not when controlling for subjective numeracy. Mediation analyses indicated that math anxiety may undermine risk comprehension in 3 ways, including through 1) objective numeracy, 2) subjective numeracy, and 3) objective and subjective numeracy in serial, with subjective numeracy mediating the association between objective numeracy and risk comprehension. Findings did not differ by domain. Conclusions. Math anxiety, objective numeracy, and subjective numeracy are associated with risk comprehension through unique pathways. Education initiatives for improving health risk comprehension may be most effective if jointly aimed at tackling numerical ability as well as negative emotions and self-evaluations related to numeracy.

To cite this article: Ludovico Minati , Camila Campanhã , Hugo D. Critchley & Paulo Sérgio Boggio (2012) Effects of transcranial direct-current stimulation (tDCS) of the dorsolateral prefrontal cortex (DLPFC) during a mixed-gambling risky decision-making task, Cognitive Neuroscience, 3:2, 80-88,

Credit risk is crucial to understanding banks’ production technology and should be explicitly accounted for when modeling the latter. The banking literature has largely accounted for risk by using ex-post realizations of banks’ uncertain outputs and the variables intended to capture risk. This is equivalent to estimating an ex-post realization of bank’s production technology which, however, may not reflect optimality conditions that banks seek to satisfy under uncertainty. The ex-post estimates of technology are likely to be biased and inconsistent, and one thus may call into question the reliability of the results regarding banks’ technological characteristics broadly reported in the literature. However, the extent to which these concerns are relevant for policy analysis is an empirical question. In this paper, we offer an alternative methodology to estimate banks’ production technology based on the ex-ante cost function. We model credit uncertainty explicitly by recognizing that bank managers minimize costs subject to given expected outputs and credit risk. We estimate unobservable expected outputs and associated credit risk levels from banks’ supply functions via nonparametric kernel methods. We apply this framework to estimate production technology of U.S. commercial banks during the period from 2001 to 2010 and contrast the new estimates with those based on the ex-post models widely employed in the literature.

There is mounting evidence that increasing natural resource exploitation (e.g., fossil fuel extraction and consumption) could trigger irreversible dramatic ecological events like global warming. While capacity investment costs and the possibility to produce at full capacity are two factors that critically affect the exploitation rate, little is known about their effect on management. I generalize standard models of pollution control under the threat of dramatic regime shifts to investigate how optimal management changes with both factors. My analysis reveals that accounting for such factors gives rise to investment and emissions policies that challenge conventional wisdom. For instance, I find that under reasonable conditions, an exogenous threat of a doomsday event induces a cautious management strategy. Using parameters estimated from climatic data, my analysis shows that raising the discount rate can induce lower emissions, highlighting the complex interplay between the threat and both factors.

We propose an extension of the framework developed by Professor Kenneth J. Arrow, for the analysis of choice under risk by an individual, hereafter referred to as a decision maker. The framework is based on the state dependent rankings of alternatives of the decision maker. We begin by showing that the existing model of decision making under uncertainty due to Professor Edi Karni can be accommodated in our framework. We provide several examples to illustrate meaningful possibilities in the model proposed here. In a final section of the paper we provide an axiomatic characterization of the Probabilistic Borda Rule based on Anonymity and a Maximal Coherence assumption, the latter being a minor variant of a similar property due to Professor Bruno De Finetti in his philosophy of probability theory.

To investigate the influence of the sense of psychological power on decision making under risk, we conducted an experiment with 60 participants and found evidence which suggests that a heightened sense of power results in excessive risk-taking. We primed the experimental group with a high-power mindset and the control group with a neutral mindset and asked participants to answer a series of hypothetical questions on expected value. The results of a chi-square test suggest that participants who were primed with a heightened sense of power focus on high but unlikely rewards. When the potential reward was greater than the loss, power-primed people were swayed towards the rewards despite the unfavorable probabilities. We propose that there is a link between a heightened sense of power and suboptimal economic decision making, and model this in the Prospect Theory framework.

In this paper we show that three conditions due to Pattanaik, when satisfied by a given profile of state-dependent preferences (linear orders) on a given and fixed set of alternatives and a probability distribution with which the various states of nature occur, are individually sufficient, for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half. Prior to this, we show that since each axiom individually implies Sen-Coherence, then, as a consequence of a result obtained earlier, each axiom along with asymmetry of the ‘preferred with at probability at least half” relation implies the transitivity of the relation. All the sufficient conditions discussed here are required to be applicable at least to all those otherwise relevant events that have positive probability. This observation also applies to a sufficient condition for the non-emptiness of the set of alternative(s) which are individual...

Several authors have recently addressed the question of whether cumulative prospect theory (CPT) resolves the St. Petersburg Paradox (Blavatskyy, 2005; Rieger & Wang, 2006). These authors show that direct application of CPT to the St. Petersburg gamble fails to resolve the paradox under most conventional CPT parameterizations. They also propose a number of remedial fixes to CPT, central among which is a constraint on the value function exponent to be smaller than the probability weighting function exponent (α < γ). As this constraint is violated by most experimentally determined CPT parameterizations,1 the remedy amounts to a fundamental reparameterization of CPT.

Background: Projections of health risks of climate change are surrounded with uncertainties in knowledge. Understanding of these uncertainties will help the selection of appropriate adaptation policies. Methods: We made an inventory of conceivable health impacts of climate change, explored the type and level of uncertainty for each impact, and discussed its implications for adaptation policy. A questionnaire-based expert elicitation was performed using an ordinal scoring scale. Experts were asked to indicate the level of precision with which health risks can be estimated, given the present state of knowledge. We assessed the individual scores, the expertise-weighted descriptive statistics, and the argumentation given for each score. Suggestions were made for how dealing with uncertainties could be taken into account in climate change adaptation policy strategies. Results: The results showed that the direction of change could be indicated for most anticipated health effects. For several potential effects, too little knowledge exists to indicate whether any impact will occur, or whether the impact will be positive or negative. For several effects, rough 'order-of-magnitude' estimates were considered possible. Factors limiting health impact quantification include: lack of data, multi-causality, unknown impacts considering a high-quality health system, complex cause-effect relations leading to multi-directional impacts, possible changes of present-day response-relations, and difficulties in predicting local climate impacts. Participants considered heat-related mortality and non-endemic vector-borne diseases particularly relevant for climate change adaptation.

This report draws on the insights of, and debate among, former high-level nuclear decision-makers and current officials at a virtual pilot-workshop held in January 2021 exploring the possible impact of predominantly aggregate technologies on nuclear weapon decision-making.

Given a profile of state-dependent evaluation functions and a probability distribution over states of nature an extended choice functional associates to it a non-empty set of chosen alternatives. The outcome that is associated to each state-dependent data may depend on the probability distribution in a non-trivial manner. The expected utility choice functional assigns to each given state-dependent data the non-empty set of alternatives obtained by maximizing expected utility. The purpose of this paper is to obtain an axiomatic characterization of the expected utility choice functional using purely combinatorial techniques.

—We present a model for supporting scoping decisions that is based on an analysis of the ROI for a given feature. Employing a ROI threshold value for making scoping decisions, the utility of the model was investigated using data from a single large project and identified a group of outlying features responsible for a disproportionate wasted investment. These initial results are promising and indicate that further investigation and validation efforts are warranted.