We conduct a standardized survey on risk preferences in 53 countries worldwide and estimate cumulative prospect theory parameters from the data. The parameter estimates show that significant differences on the cross-country level are to some extent robust and related to economic and cultural differences. In particular, a closer look on probability weighting underlines gender differences, economic effects, and cultural impact on probability weighting. The data set is a useful starting point for future research that investigates the impact (...) of risk preferences on the market level. (shrink)

Much behavioral welfare economics assumes that expected utility theory does not accurately describe most human choice under risk. A substantial literature instead evaluates welfare consequences by taking cumulative prospect theory as the natural default alternative, at least where description is concerned. We present evidence, based on a review of previous literature and new experimental data, that the most empirically adequate hypothesis about human choice under risk is that it is heterogeneous, and that where EUT does not (...) apply, more choice is characterized by rank-dependent utility models than by CPT. Most of the apparently loss-averse choice behavior results from probability weighting rather than from direct disutility experienced when an outcome is framed as a loss against an idiosyncratic reference point. We then consider implications of this finding for methodological debates about how to model welfare effects of policies, and argue that abandonment of a dogmatic belief in CPT as the correct theory of risk human choice exposes a conceptual error that is widespread in behavioral welfare economics. We provide concluding reflections on second-order, philosophical issues around the grounding of normative commitments in policy-focused economics. (shrink)

In this paper, we analyse higher-order risky choices by the representative cumulative prospect theory (CPT) decision maker from three alternative reference points. These are the status quo, average payout and maxmin. The choice tasks we consider in our analysis include binary risks, and are the ones employed in the experimental literature on higher order risk preferences. We demonstrate that the choices made by the representative subject depend on the reference point. If the reference point is the status (...) quo and the lottery choices exhibit symmetric risk, we demonstrate that there is no third order reflection effect of lottery choices but there is a fourth order reflection effect. When the average payout is the reference point, we demonstrate that any third or fourth order lottery choice is possible dependent upon the lottery payoffs. However, under the assumption of maxmin reference point, the risky choices are prudent and temperate. In addition to these results, our analysis reveals that the representative CPT subject can choose combinations of second with third and fourth order risky options that differ from those in other major models of decision under risk. We contrast our theoretical predictions with the empirical results reported in the literature on higher order risk preferences and are able to reconcile some conflicting experimental evidence. (shrink)

Cumulative Prospect Theory (CPT) does not explain the St. Petersburg Paradox. We show that the solutions related to probability weighting proposed to solve this paradox, (Blavatskyy, Management Science 51:677–678, 2005; Rieger and Wang, Economic Theory 28:665–679, 2006) have to cope with limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting functions generally proposed in the literature by another specification which respects the following properties: (1) to solve the (...) paradox, the slope at zero has to be finite. (2) to account for the fourfold pattern of risk attitudes, the probability weighting has to be strong enough. (shrink)

Original and cumulative prospect theory differ in the composition rule used to combine the probability weighting function and the value function. We test the predictive power of these composition rules by performing a novel out-of-sample prediction test. We apply estimates of prospect theory’s weighting and value function obtained from two-outcome cash equivalents, a domain where original and cumulative prospect theory coincide, to three-outcome cash equivalents, a domain where the composition rules of the (...) two theories differ. Although both forms of prospect theory predict three-outcome cash equivalents very well, at the aggregate level, we find small but systematic under-prediction of cash equivalents for cumulative prospect theory and small but systematic over-prediction of cash equivalents for original prospect theory. We also observe substantial heterogeneity across subjects and types of gambles, some of which is accounted for by differences in the curvature and elevation of the weighting function across individuals. We also find differences in prediction related to whether the worst outcome is zero or non-zero. (shrink)

Third generation prospect theory is a theory of choices and of judgments of highest buying and lowest selling prices of risky prospects, i.e., of willingness to pay and willingness to accept. The gap between WTP and WTA is sometimes called the “endowment effect” and was previously called the “point of view” effect. Third generation prospect theory combines cumulative prospect theory for risky prospects with the theory that judged values are based on (...) the integration of price paid or price received with the consequences of gambles. In TGPT, the discrepancy between WTP and WTA is due to loss aversion-losses have greater absolute utility than gains of the same value. TGPT was developed independently of similar developments by Birnbaum and Zimmermann :145–187, 1998) and Luce. This paper reviews theoretical and empirical findings, to show that TGPT fails as a descriptive model of both choices and judgments. Evidence refutes three implications of TGPT, but they are consistent with configural weight models in which loss aversion is not needed to describe the results. In the configural weight models, buyers place greater weight on lower consequences, attributes or estimates of value compared to sellers, who place greater configural weight on higher aspects of an object or prospect. (shrink)

Are risk preferences stable over time? To address this question we elicit risk preferences from the same pool of subjects at two different moments in time. To interpret the results, we use a Fechner stochastic choice model in which the revealed preference of individuals is governed by some underlying preference, together with a random error. We take cumulative prospect theory as the underlying preference model (Kahneman and Tversky, Econometrica 47:263–292, 1979; Tversky and Kahneman, Journal of Risk and (...) Uncertainty 5:297–323, 1992). We observe that the aggregate pattern of preferences is very similar in both sessions, and it matches the results reported in the literature. Most subjects are risk averse for gains, and risk seeking for losses. However, the subjects that jointly agree with the reflection effect of prospect theory are around 50%. The percentage of individuals that change their responses across sessions is quite high, 63%. Estimating the stochastic choice model we find that 72% of the subjects have an underlying preference which agrees with the reflection effect of prospect theory. The remaining 28% are mainly classified as risk averse for both gains and losses. The results reinforce the empirical validity of the reflection effect. Deviations from the reflection effect can be attributed to noise, as well as to the existence of a fraction of risk averse subjects. (shrink)

Cumulative Prospect Theory is the modern version of Prospect Theory and it is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e., the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assumption of the theory, proposing new paradoxes where the Gain-Loss Separability is violated. We present a generalization of Cumulative Prospect (...) class='Hi'>Theory which does not imply Gain-Loss Separability and is able to explain the cited paradoxes. On the other hand, the new model, which we call the bipolar Cumulative Prospect Theory, genuinely generalizes the original Prospect Theory of Kahneman and Tversky, preserving the main features of the theory. We present also a characterization of the bipolar Choquet Integral with respect to a bi-capacity in a discrete setting. (shrink)

This study extends experimental tests of (cumulative) prospect theory (PT) over prospects with more than three outcomes and tests second-order stochastic dominance principles (Levy and Levy, Management Science 48:1334–1349, 2002; Baucells and Heukamp, Management Science 52:1409–1423, 2006). It considers choice behavior of people facing prospects of three different types: gain prospects (losing is not possible), loss prospects (gaining is not possible), and mixed prospects (both gaining and losing are possible). The data supports the distinction of risk behavior (...) into these three categories of prospects, Further, probability weighting and diminishing sensitivity of utility as predicted by PT are observed. Loss aversion is, however, less pronounced, except for choices where one prospect is degenerate. The data suggests that the probability of losing may be relevant for loss aversion. (shrink)

Balancing the pros and cons of two options is undoubtedly a very appealing decision procedure, but one that has received scarce scientific attention so far, either formally or empirically. We describe a formal framework for pros and cons decisions, where the arguments under consideration can be of varying importance, but whose importance cannot be precisely quantified. We then define eight heuristics for balancing these pros and cons, and compare the predictions of these to the choices made by 62 human participants (...) on a selection of 33 situations. The Levelwise Tallying heuristic clearly emerges as a winner in this competition. Further refinements of this heuristic are considered in the discussion, as well as its relation to Take the Best and Cumulative Prospect Theory. (shrink)

This paper merges the non-expected utility approach (Tversky and Kahneman, J Risk Uncertain 5:297–323, 1992 and Quiggin, J Econ Behav Organ 3:323–343, 1982) into Akerlof’s (Quart J Econ 84:488–500, 1970) model of Market for Lemons. We derive the results for different probability weighting functions and analyze the phenomenon of market failure in light of non-expected utility maximization. Our main finding suggests that when the proportion of traded lemons is high (low), the problem of market failure is mitigated (enhanced). In addition, (...) for the case of Cumulative Prospect Theory, we show that (a) the higher the loss aversion is, the more pronounced is the market failure; (b) gain-domain elevation is negatively related to the extent of market failure; and (c) the value function is (i) negatively monotonic in the gain-domain diminishing sensitivity parameter when the market is characterized by a high proportion of “peaches,” and (ii) positively monotonic in the loss-domain diminishing sensitivity parameter when the market is characterized by a high proportion of “lemons.”. (shrink)

Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. First, a (...) probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent method. (shrink)

Mathematical realists have long invoked the categoricity of axiomatizations of arithmetic and analysis to explain how we manage to fix the intended meaning of their respective vocabulary. Can this strategy be extended to set theory? Although traditional wisdom recommends a negative answer to this question, Vann McGee (1997) has offered a proof that purports to show otherwise. I argue that one of the two key assumptions on which the proof rests deprives McGee's result of the significance he and the (...) realist want to attribute to it. I consider two strategies to deal with the problem --- one of which is outlined by McGee himself (2000) --- and argue that both of them fail. I end with some remarks on the prospects for mathematical realism in the light of my discussion. (shrink)

There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, (...) 1988c) ‘consequentialist’ argument for the SEU preference axioms, but go on to formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted. (shrink)

This paper presents an axiomatic framework for the priority heuristic, a model of bounded rationality in Selten’s (in: Gigerenzer and Selten (eds.) Bounded rationality: the adaptive toolbox, 2001) spirit of using empirical evidence on heuristics. The priority heuristic predicts actual human choices between risky gambles well. It implies violations of expected utility theory such as common consequence effects, common ratio effects, the fourfold pattern of risk taking and the reflection effect. We present an axiomatization of a parameterized version of (...) the heuristic which generalizes the heuristic in order to account for individual differences and inconsistencies. The axiomatization uses semiorders (Luce, Econometrica 24:178–191, 1956), which have an intransitive indifference part and a transitive strict preference component. The axiomatization suggests new testable predictions of the priority heuristic and makes it easier for theorists to study the relation between heuristics and other axiomatic theories such as cumulative prospect theory. (shrink)

In comparing different risk elicitation methods under the assumptions of expected utility theory, previous studies have found significant differences in the elicited risk attitudes. This paper extends this line of research to consider cumulative prospect theory by comparing risk attitudes and probability weightings determined using two elicitation methods: the method by Tanaka et al. :557–571, 2010; TCN method) and the method by Wakker and Deneffe :1131–1150, 1996; WD method). We demonstrate that the two methods reveal significantly (...) different mean values for the measured risk attitudes. Participants are classified on average as moderately risk-averse using the TCN method, whereas the same individuals are classified as nearly risk-neutral using the WD method. Moreover, we find that on average, participants overweight low probabilities and underweight high probabilities to a greater extent with the WD method than with the TCN method. Therefore, the different elicitation methods, that both consider probability weighting, can lead to different measured values of risk attitude and probability weighting. (shrink)

In this article, we show that behavioral features can be obtained at a group level even if they do not appear at the individual level. Starting from a standard model of Pareto optimal allocations, with expected utility maximizers but allowing for heterogeneity among individual beliefs, we show in particular that the representative agent has an inverse S-shaped probability distortion function as in Cumulative prospect theory.

It is widely held that the influence of risk on rational decisions is not entirely explained by the shape of an agent’s utility curve. Buchak (Erkenntnis, 2013, Risk and rationality, Oxford University Press, Oxford, in press) presents an axiomatic decision theory, risk-weighted expected utility theory (REU), in which decision weights are the agent’s subjective probabilities modified by his risk-function r. REU is briefly described, and the global applicability of r is discussed. Rabin’s (Econometrica 68:1281–1292, 2000) calibration theorem strongly (...) suggests that plausible levels of risk aversion cannot be fully explained by concave utility functions; this provides motivation for REU and other theories. But applied to the synchronic preferences of an individual agent, Rabin’s result is not as problematic as it may first appear. Theories that treat outcomes as gains and losses (e.g. prospect theory and cumulative prospect theory) account for risk sensitivity in a way not available to REU. Reference points that mark the difference between gains and losses are subject to framing, many instances of which cannot be regarded as rational. However, rational decision theory may recognize the difference between gains and losses, without endorsing all ways of fixing the point of reference. In any event, REU is a very interesting theory. (shrink)

In Rawls’ influential social contract approach to distributive justice, the fair income distribution is the one that an individual would choose behind a veil of ignorance. Harsanyi treated this situation as a decision under risk and arrived at utilitarianism using expected utility theory. This paper investigates the implications of applying cumulative prospect theory instead, which better describes behavior under risk. I find that the specific type of inequality in bottom-heavy right-skewed income distributions, which includes the log-normal (...) income distribution, could be perceived as desirable. This optimal inequality result contrasts the implications of other social welfare criteria. (shrink)

The COVID-19 pandemic poses a major challenge to policy makers on how to encourage compliance to social distancing and personal protection rules. This paper compares the effectiveness of two policies that aim to increase the frequency of responsible health behavior using smartphone-tracking applications. The first involves enhanced alert capabilities, which remove social externalities and protect the users from others’ reckless behavior. The second adds a rule enforcement mechanism that reduces the users’ benefit from reckless behavior. Both strategies should be effective (...) if agents are expected-value maximizers, risk averse, and behave in accordance with cumulative prospect theory or in accordance with the Cognitive Hierarchy model. A multi-player trust-game experiment was designed to compare the effectiveness of the two policies. The results reveal a substantial advantage to the enforcement application, even one with occasional misses. The enhanced-alert strategy was completely ineffective. The findings align with the small samples hypothesis, suggesting that decision makers tend to select the options that lead to the best payoff in a small sample of similar past experiences. In the current context, the tendency to rely on a small sample appears to be more consequential than other deviations from rational choice. (shrink)

There is widespread agreement about a combination of attributes that someone needs to possess if they are to be counted as a conservative. They need to lack definite political ideals, goals or ends, to prefer the political status quo to its alternatives, and to be risk averse. Why should these three highly distinct attributes, which are widely believed to be characteristic of adherents to a significant political position, cluster together? Here I draw on prospect theory to develop an (...) explanation for the clustering of attributes that is characteristic of conservatives. I argue that a lack of political ideals is the underlying driver of conservatism. I will provide reason to believe that people who lack political ideals are disposed to prefer the political status quo to its alternatives; and reason to believe that people who prefer the political status quo to its alternatives are disposed to be risk averse, at least with respect to significantly many of the risks that arise in the social and political domain. I also consider and reject some other potential explanations for the clustering of attributes that is characteristic of conservatives and sketch some policy implications that follow from the explanation I develop. (shrink)

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide (...) variety of disciplines. The material in the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (shrink)

This paper considers a decision-making process under ambiguity in which the decision-maker is supposed to split outcomes between familiar and unfamiliar ones. She is assumed to behave differently with respect to unfamiliar gains, unfamiliar losses and customary (familiar) outcomes. In particular, she is supposed to be pessimistic on gains, optimistic on losses and ambiguity neutral on the familiar outcomes. A generalization of the usual Choquet Integral is formalized when the decision maker holds capacities and probabilities. A characterization of the decision-maker’s (...) behavior is provided for a specific subset of capacities, in which it is shown that the decision-maker underestimates the unfamiliar outcomes while is linear in probabilities on customary ones. (shrink)

Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, (...) the type-restrictions imposed by STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

We give a probabilistic justification of the shape of one of the probability weighting functions used in Prospect Theory. To do so, we use an idea recently introduced by Herzog and Hertwig. Along the way we also suggest a new method for the aggregation of probabilities using statistical distances.

In the theoretical description of prospect theory, distinct sets of parameters can control the curvature of the value function and the shape of the probability weighting function. There is one for the gain domain and one for the loss domain. However, in most estimations, behaviour over losses is assumed to perfectly reflect behaviour over gains, through a unique set of parameters. We examine the consequences of relaxing this simplifying assumption in the context of Tanaka et al.’s (Am Econ (...) Rev 100(1):557–571, 2010) risk-elicitation procedure based on multiple price lists. We show that subjects’ behaviour for gains is mostly reflected for losses at the aggregate and individual levels, and is consistent with the distinctive prospect theory fourfold pattern. Reflection is only partial as the mean curvature of the value function is slightly less convex for losses than it is concave for gains. These results are robust to a high-stake context. However, we demonstrate that assuming reflection can have huge consequences on loss-aversion measures. Incidentally, we also highlight the existence of a strong, negative and persistent pure loss-frame effect on elicited loss aversion. We recommend that future practitioners and modellers are particularly cautious about the loss-aversion values they obtain or use because these are especially sensitive to parametric assumptions and framing. (shrink)

Prospect Theory (PT) is widely regarded as the most promising descriptive model for decision making under uncertainty. Various tests have corroborated the validity of the characteristic fourfold pattern of risk attitudes implied by the combination of probability weighting and value transformation. But is it also safe to assume stable PT preferences at the individual level? This is not only an empirical but also a conceptual question. Measuring the stability of preferences in a multi-parameter decision model such as PT (...) is far more complex than evaluating single-parameter models such as Expected Utility Theory under the assumption of constant relative risk aversion. There exist considerable interdependencies among parameters such that allegedly diverging parameter combinations could in fact produce very similar preference structures. In this paper, we provide a theoretic framework for measuring the (temporal) stability of PT parameters. To illustrate our methodology, we further apply our approach to 86 subjects for whom we elicit PT parameters twice, with a time lag of 1 month. While documenting remarkable stability of parameter estimates at the aggregate level, we find that a third of the subjects show significant instability across sessions. (shrink)

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient of (...) 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome. (shrink)

The introduction of the euro gave a unique opportunity to empirically disentangle two components of utility: intrinsic value, a rational component central in economics, and the numerosity effect (going by numbers while ignoring units), a descriptive and irrational component central in prospect theory and underlying the money illusion. We measured relative risk aversion in Belgium before and after the introduction of the euro, and could consider changes in intrinsic value while keeping numbers constant, and changes in numbers while (...) keeping intrinsic value constant. Intrinsic value significantly affected risk aversion, and the numerosity effect did not. Our study is the first to confirm the classical hypothesis of increasing relative risk aversion while avoiding irrational distortions due to the numerosity effect. (shrink)

Prospect theory is increasingly used to explain deviations from the traditional paradigm of rational agents. Empirical support for prospect theory comes mainly from laboratory experiments using student samples. It is obviously important to know whether and to what extent this support generalizes to more naturally occurring circumstances. This article explores this question and measures prospect theory for a sample of private bankers and fund managers. We obtained clear support for prospect theory. Our (...) financial professionals behaved according to prospect theory and violated expected utility maximization. They were risk averse for gains and risk seeking for losses and their utility was concave for gains and convex for losses. They were also averse to losses, but less so than commonly observed in laboratory studies and assumed in behavioral finance. A substantial minority focused on gains and largely ignored losses, behavior reminiscent of what caused the current financial crisis. (shrink)

We propose a new theory to explain the nature and function of subjective experience, as a mechanism that guides the organism towards beneficial outcomes. In simple animals, that guidance takes the form of an affect producing a fitness-enhancing response. In human consciousness, there is not a single response, but a range of potential developments allowing a free choice. That range can be modelled as a local prospect: a field of possibilities centred on the present situation and coloured by (...) valence. Building on neural models of global workspace and adaptive resonance, we suggest how such a prospect could be implemented in the brain: as a halo of activation diffusing from, and feeding back into, a core of circulating activation. Using the thought experiment of qualia inversion, we argue that local prospect theory solves the ‘hard problem of consciousness’. We show how our theory explains key characteristics of consciousness: subjectivity, feeling, free will, agency, transience, continuity, integration, selectivity, intentionality, and ‘what it is like’. (shrink)

Modal structuralism promises an interpretation of set theory that avoids commitment to abstracta. This article investigates its underlying assumptions. In the first part, I start by highlighting some shortcomings of the standard axiomatisation of modal structuralism, and propose a new axiomatisation I call MSST (for Modal Structural Set Theory). The main theorem is that MSST interprets exactly Zermelo set theory plus the claim that every set is in some inaccessible rank of the cumulative hierarchy. In the (...) second part of the article, I look at the prospects for supplementing MSST with a modal structural reflection principle, as suggested in Hellman (2015). I show that Hellman’s principle is inconsistent (Theorem 5.32), and argue that modal structural reflection principles in general are either incompatible with modal structuralism or extremely weak. (shrink)

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient of (...) 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome. (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are (...) characterized by objective probabilities). Our new elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

We investigate whether the display of portfolio performance as coming from one large portfolio or two smaller subportfolios matters to individuals and whether prospect theory can explain this preference. To this end, we run a large survey experiment of 3267 individuals in 5 European countries presenting an identical overall return as coming from one portfolio or two smaller subportfolios to individuals. We also elicited the coefficients of the prospect theory value function through price list lotteries. In (...) losses, following prospect theory and mental accounting predictions, we observe emprically a preference for the display of returns as coming from 2 subportfolios, one displaying a small gain and the other a large loss, over a unique portfolio displaying the aggregated resulting loss. As expected, for an overall gain, individuals favor one portfolio over two subportfolios, one displaying a small loss and the other a larger gain. The shape of the value function does not explain individuals’ preferences. The reference point seems to be the main factor involved in explaining individuals’ choice of two subportfolio presentations of the outcome. (shrink)

Prospect theory is an alternative theory of choice under conditions of risk, and deviates from expected utility theory by positing that people evaluate choices with respect to gains and losses from a reference point. They tend to overweight losses with respect to comparable gains and engage in risk-averse behavior with respect to gains and risk-acceptant behavior with respect to losses. They also respond to probabilities in a non-linear manner. I begin with an overview of prospect (...) theory and some of the evidence upon which it is based, and then consider some of the implications of the theory for American politics, international relations, and the law. I end with a brief discussion of some of the conceptual and methodological problems confronting the application of prospect theory to the study of politics. (shrink)

Investors who are more willing to accept risks when evaluating their investments less frequently are said to exhibit myopic loss aversion (MLA). Several recent experimental studies found that, on average, subjects bet significantly higher amounts on a risky lottery when they observe only a cumulative outcome of several realizations of the lottery (long evaluation period). In this article, we reexamine these empirical findings by analyzing individual rather than aggregate choice patterns. The behavior of the majority of subjects is inconsistent (...) with the hypothesis of MLA: they bet an intermediate fraction of their initial endowment and these bets, on average, are not significantly different across two treatments with short and long evaluation period. We discuss several alternative explanations of this finding, including the Fechner model of random errors and the financial asset pricing model. (shrink)

Whereas original prospect theory was introduced over 40 years ago, its formula for multi-outcome prospects has never yet been published, resulting in many misunderstandings. This note provides that formula.

_Purpose__._ The basis of the presented study is a methodological and human-centred analysis of the philosophy of education of the outstanding Ukrainian educator Vasyl Sukhomlynskyi as a relevant anthropological-intellectual strategy for understanding and comprehending the educational process in the context of civilisation challenges. This implies a sequential solution to the following tasks: 1) to review the conceptual content and human-centred load of Vasyl Sukhomlynskyi’s pedagogical position in the discourses of philosophical anthropology and social philosophy; 2) to analyse the theoretical knowledge (...) of the anthropo-existential concept of the outstanding teacher in the context of the transformation of Ukrainian education; 3) to determine the main parameters of the cognitive field of Sukhomlynskyi’s philosophy of education in the development of values of patriotic education of young people. _Theoretical__ basis__._ The dynamic process of Ukraine’s unfolding struggle for the preservation of its nation and territorial integrity brings Sukhomlynskyi’s philosophy of education to a new level of understanding of human life and society. The human-centred dimension in interaction with the philosophy of education allows us to define Sukhomlynskyi’s pedagogical concept in the fullness of its metaphilosophical, existential and axiological content. The relevance of the problem under study is due to the crisis of values in the situation of civilizational transformations, which, as a result of information and digital technologies, have a cumulative impact on all spheres of people’s life and their attitude to the world. In the process of implementing the educational ideas of the Ukrainian teacher, the development and transformation of the individual’s self-awareness takes place in accordance with the intellectual challenges of the modern socio-cultural environment. _Originality._ It is substantiated that the philosophy of education of Vasyl Sukhomlynskyi largely determines the strategy for the transformation of Ukrainian education both in the context of digitalisation of the educational space and in the situation of a full-scale war against Russian aggression, which opens up new prospects for the implementation of identity dimensions in interaction with a qualitatively different level of national subjectivity. _Conclusions__._ The approval of the conceptual provisions of Sukhomlynskyi’s philosophy of education gives rise to a new type and method of paradigm of thinking and cognition in the implementation of strategies for the transformation of modern education, which determine the qualitative theory of the educational process in the context of human-centrism. It is characterized by the level of modern philosophical reflections, which allows preserving and at the same time changing the system of education and upbringing of the young generation in the context of universal values. On this basis, the philosophy of education of the prominent Ukrainian educator appears as a way of renewing all aspects of human life, which deconstructs itself in the situation of a human-centric dimension. (shrink)

We discuss the bearing of Daniel Kahneman and Amos Tversky's Prospect Theory on some central issues in ethics. It has been argued that the theory provides a better explanation of our intuitive responses to some important ethical decision cases—like some famous cases put by Philippa Foot and others—than traditional and widely acknowledged ethical principles do. In this way, Prospect Theory contributes to the new wave of skepticism, emanating from the social sciences, about the role of (...) intuitive judgments in ethical theory and philosophy more generally. We focus on Kahneman and Tversky's famous Asian Disease Problem. We show that the case fails to support Prospect Theory over traditional ethical theory as an explanation of the most common intuitive responses to the case, and, moreover, fails as an account of the most common intuitive responses to Foot's famous trolley case and related cases. We maintain that careful critical attention to all these cases shows that Prospect Theory has not made a successful incursion into ethics, whatever it may have established about non-ethical decision-making. (shrink)

_Purpose._ The basis of the presented research is a philosophical and methodological analysis of the human-centrism concept as a new intellectual strategy of comprehending and understanding the prospects of human existence in a situation of information-digital reality, which provides for the consistent solution of the following problems: 1) to make an explication of the conceptual content and semantic loading of human-centrism in the discourses of social philosophy and philosophical anthropology; 2) to analyse the theoretical significance and methodological role of human-centrism (...) in the information-digital reality; 3) to characterize the main parameters of the problematic field of human-centrism in overcoming the crisis of identity and preserving the system of universal human values. _Theoretical basis__._ The objective logic of unfolding of the modern information-digital world transforms philosophical anthropology into a new level of comprehending the human existence. Human-centrism interacts with philosophical anthropology and evaluates it from the point of its metaphilosophical, axiological-existential and methodological content. The assertion of human-centrism is caused by the identity crisis in the context of civilizational transformations, which as a result of the cumulative effect of information technology have a powerful influence on all aspects of human life and thinking. The philosophy of human-centrism as a life-affirming factor determines the development and adaptation of human self-consciousness to the modern socio-cultural environment, determined by information and technological processes. _Originality__._ It is substantiated that human-centrism as a new strategy of modern philosophical and anthropological discourses opens new cognition perspectives of the essence of human in the information-digital reality and contributes to the construction and implementation of new dimensions of identity in interaction with a qualitatively different level of world attitude. _Conclusions__._ The assertion of information-digital reality gives rise to a new type of philosophical and anthropological paradigm, a qualitative manifestation of which is the theory and methodology of human-centrism. It is characterized by a modern level of philosophical reflection, which allows preserving and at the same time renewing the system of universal human values. On this basis, human-centrism is a way of complementarity of all aspects of human life, who reconstructs themselves in a situation of new anthropological dimensions. (shrink)

We investigate two formalizations of Optimality Theory, a successful paradigm in linguistics.We first give an order-theoretic counterpart for the data and processinvolved in candidate evaluation.Basically, we represent each constraint as a function that assigns every candidate a degree of violation.As for the second formalization, we define (after Samek-Lodovici and Prince) constraints as operations that select the best candidates out of a set of candidates.We prove that these two formalizations are equivalent (accordingly, there is no loss of generality with using (...) violation marks and dispensing with them is only apparent).Importantly, we show that the second formalization is equivalent with a class of operations over sets of formulas in a given logical language.As a result, we prove that Optimality Theory can be characterized by certain cumulative logics.So, applying Optimality Theory is shown to be reasoning by the rules of cumulative logics. (shrink)

Naturalistic ethics is the reigning paradigm among contemporary ethicists; in God and Cosmos, Baggett and Walls argue that this approach is seriously flawed. This book canvasses a broad array of secular and naturalistic ethical theories in an effort to test their adequacy in accounting for moral duties, intrinsic human value, prospects for radical moral transformation, and the rationality of morality. In each case, the authors argue, although various secular accounts provide real insights and indeed share common ground with theistic ethics, (...) the resources of classical theism and orthodox Christianity provide the better explanation of the moral realities under consideration. Among such realities is the fundamental insight behind the problem of evil, namely, that the world is not as it should be. Baggett and Walls argue that God and the world, taken together, exhibit superior explanatory scope and power for morality classically construed, without the need to water down the categories of morality, the import of human value, the prescriptive strength of moral obligations, or the deliverances of the logic, language, and phenomenology of moral experience. This book thus provides a cogent moral argument for God's existence, one that is abductive, teleological, and cumulative. (shrink)

This volume, stemming from the annual meeting of the Theory Section of the American Sociological Association, addresses theoretical cumulation in two senses: } the rigorous empirical testing of theoretical models } the synthesis, extension and consolidation of the existing theoretical base of the discipline. This distinguished group of contributors, all leading scholars, have expanded upon the wisdom of the giants of theoretical sociology, and creatively broadened the base of theory in the field. Through the description and analysis of (...) their own theoretical programmes, they show that the cumulation of theory is possible in sociology and point the directions and methods this cumulation should take. (shrink)

Primitivists about truth maintain that truth cannot be analysed in more fundamental terms. Defences of primitivism date back to the early years of analytic philosophy, being offered by G.E. Moore, Bertrand Russell, and Gottlob Frege. In more recent years, a number of contemporary philosophers—including Donald Davidson, Ernest Sosa, Trenton Merricks, Douglas Patterson, and Jamin Asay—have followed suit, defending their own versions of primitivism. I'll begin by offering a brief history of primitivism, situating each of these views within the landscape of (...) primitivist truth theories and detailing some of their core motivations and apparent shortcomings. To close the discussion, I'll offer a diagnosis of the prospects of primitivism, focusing on the mystery challenge, which has loomed large throughout the history of primitivist truth theories, and the methodology that should be used in evaluating primitivist (and other) truth theories going forward. (shrink)

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing (...) principle, known as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness theorem for K∞α is proved by the method of reduction trees, and it is shown that every model of K∞α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first-order set theories can be interpreted in K∞α, for suitable α.