Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting

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.     

Time,bounded utility,and the St. Petersburg paradox

The assumption of bounded utility function resolves the St. Petersburg paradox. The justification for such a bound is provided by Brito, who argues that limited time will bound the utility function. However, a reformulated St. Petersburg game, which is played for both money and time, effectively circumvents Brito's justification for a bound. Hence, no convincing justification for bounding the utility function yet exists.     

The St. Petersburg gamble and risk

Pursuing a line of thought initiated by Maurice Allais (1979), I consider whether the mean-risk method of decision making introduced by Harry Markowitz (1959) and other resolves Karl Menger's (1934) version of the St. Petersburg paradox. I provide a conditional answer to this question. I demonstrate that given certain plausible assumption about attitudes toward risk, a certain plausible development of the mean-risk method does resolve the paradox. My chief premiss is roughly that in the St. Petersburg gamble the small chances for large prizes create big risks.     

Natural Resource Management

Human qualities are one of the most important components of a society's culture, characterizing its stability and potential for reform and, to a considerable extent, determining the well-being of the people themselves. This is a field that has hardly been touched upon as an object of sociological research. Only a few works have focused on this issue: a population's social quality is analyzed as one of the regulators of the social mechanism of the development of the economy [1], emphasizing the qualities of the working person as an element of the economic culture; another work studies the quality of the population of St. Petersburg [2]. Fundamental research is being done by candidate of philosophical sciences G. M. Kochetov, who has compiled a glossary of human qualities and properties comprising about 75,000 terms [3].     

Testing the Intransitivity Explanation of the Allais Paradox

This paper uses a two-dimensional version of a standard common consequence experiment to test the intransitivity explanation of Allais-paradox-type violations of expected utility theory. We compare the common consequence effect of two choice problems differing only with respect to whether alternatives are statistically correlated or independent. We framed the experiment so that intransitive preferences could explain violating behavior when alternatives are independent, but not when they are correlated. We found the same pattern of violation in the two cases. This is evidence against intransitivity as an explanation of the Allais Paradox. The question whether violations of expected utility are mainly due to intransitivity or to violation of independence is important since it is exactly on this issue the main new decision theories differ.     

Feddersen and Pesendorfer meet Ellsberg

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis (Theor Econo 11(3): 865–895, 2016) shows that when voters have ambiguous prior beliefs—a (closed, convex) set of priors—and follow maxmin expected utility (MEU), such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead to posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error (such as conviction in jury trials). In a classical model, Feddersen and Pesendorfer (Am Politi Sci Rev 92(1):23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis (Theor Econo 11(3): 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals.

     

Introspective utility and the group choice problem

This paper presents empirical evidence somewhat supportive of the hypothesis that von Neumann-Morgenstern utility and so-called ‘introspective utility’ are intrinsically the same. In other words, this evidence is somewhat supportive of theview that the Allais Paradox and related phenomena are more apparent than real. The bearing that this evidence has on the relationship between two methods of group choice is discussed.     

On the Conditional Value-at-Risk probability-dependent utility function

The Expected Shortfall or Conditional Value-at-Risk (CVaR) has been playing the role of main risk measure in the recent years and paving the way for an enormous number of applications in risk management due to its very intuitive form and important coherence properties. This work aims to explore this measure as a probability-dependent utility functional, introducing an alternative view point for its Choquet Expected Utility representation. Within this point of view, its main preference properties will be characterized and its utility representation provided through local utilities with an explicit dependence on the assessed revenue’s distribution (quantile) function. Then, an intuitive interpretation for the related probability dependence and the piecewise form of such utility will be introduced on an investment pricing context, in which a CVaR maximizer agent will behave in a relativistic way based on his previous estimates of the probability function. Finally, such functional will be extended to incorporate a larger range of risk-averse attitudes and its main properties and implications will be illustrated through examples, such as the so-called Allais Paradox.     

更富裕是否意味着更幸福?基于横截面时间序列数据的分析(2003-2013)

四十年前,经济学家伊斯特林提出了“幸福感悖论”:短时期内个人和国家的财富水平与幸福感都正向相关,而在长期背景下,经济增长并不会显著提高整体幸福感水平。本文使用横跨十年的全国代表性横截面时间序列数据直接检验了财富与幸福感的关系,结果证实了“幸福感悖论”。研究发现,虽然在短时期内,无论是家庭人均收入还是省份的人均生产总值都与幸福感有显著的正相关,但在经济高速发展的十年内(2003-2013),省份人均生产总值的变化与幸福感的变化之间并没有显著相关。     

Survival through the Allais paradox

This paper investigates the allegation that behavior such as the Allais Paradox reduces the probability of survival. Examples are demonstrated where maximizing probability of survival in two choice situations imply a set of choices that add up to the Allais Paradox.     

Risk taking on behalf of others: The role of social distance

Individuals take decisions on behalf of others in many different contexts. In this paper, we focus on lotteries with negative expected value and study if (and how) risky choices made on behalf of another person differ i) compared to decisions which do not affect anyone else, and ii) depending on the social distance between who makes the decision and who is affected by it. Our results show that social distance (i.e., whether the person affected by one’s decision is an unknown stranger or a friend) is an important determinant when people decide on behalf of others. Moreover, when deciding on behalf of a friend rather than only for themselves or a stranger, average individual behavior is closer to expected value maximization, exhibiting less risk taking. These findings suggest that responsibility for others’ outcome and the empathy gap affect the decision making process, particularly when the social distance is shortened. The results are robust to different feedback frequencies. Controlling for order effects shows that experiencing a decrease in social distance is crucial in activating this mechanism.     

Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences*

Many studies have considered the probability that a pairwise majority rule (PMR) winner exists for three candidate elections. The absence of a PMR winner indicates an occurrence of Condorcet's Paradox for three candidate elections. This paper summarizes work that has been done in this area with the assumptions of: Impartial Culture, Impartial Anonymous Culture, Maximal Culture, Dual Culture and Uniform Culture. Results are included for the likelihood that there is a strong winner by PMR, a weak winner by PMR, and the probability that a specific candidate is among the winners by PMR. Closed form representations are developed for some of these probabilities for Impartial Anonymous Culture and for Maximal Culture. Consistent results are obtained for all cultures. In particular, very different behaviors are observed for odd and even numbers of voters. The limiting probabilities as the number of voters increases are reached very quickly for odd numbers of voters, and quite slowly for even numbers of voters. The greatest likelihood of observing Condorcet's Paradox typically occurs for small numbers of voters. Results suggest that while examples of Condorcet's Paradox are observed, one should not expect to observe them with great frequency in three candidate elections.     

韦伯“英国法悖论”的理性观反思

韦伯的"英国法悖论",是指按韦伯的理性化标准,英国法的理性化是程度较低的.然而事实上英国法又能较好地保障英国人的确定性、自由和秩序."英国法悖论"的产生,在于韦伯将理论理性视为唯一的理性并将其作为标准尺度来衡量英国法.事实证明,英国法的实践理性不但是一种理性化道路,而且是一种较为合理的理性化之路.反倒是韦伯的理论理性存在诸多问题.因此,需要认真反思韦伯的理论理性法治观.     

Recuerdos de Nuestro Pasado

Following is an interview with Erin Segal, group worker and coauthor of Recuerdos de Nuestro Pasado (Memories of our Past), a multivocal memoir about growing up in El Salvador and growing old in Washington DC, which emerged from a storytelling group at Mary’s Center’s Bernice Fonteneau Senior Wellness Center. The group members and coauthors are Angela Celaya, Sergio Guzmán, Jose Lovos, and Gloria Revelo. Using alternating English-language stanzas, the book expresses the life stories of four senior citizens and includes the images of their photographs and objects as well as illustrations by the book designer Julie Cho. Segal and Cho are cofounders of Thick Press. All profit from this book will go to St. Jude Children’s Hospital.     

Pascal’s and Tabarrok’s Wagers

In a recent paper A. Tabarrok [Believe in Pascal’s Wager? Have I Got a Deal for You!, Theory and Decision 48, 123--128, 2000] argued that a believer who accepts Pascal’s Wager should in addition accept payment of any given fee in return for a given increase in the probability of reaching God. However the conclusion is obtained from manipulations of infinities which are not valid in an expected utility model. In this note, an alternative model is formulated in which Tabarrok’s conclusion can be obtained.     

The curse of hope

In K?szegi and Rabin’s (Q J Econ 1133–1165, 2006, Am Econ Rev 97:1047–1073, 2007) reference-dependent model of preferences, the chance of obtaining a better outcome can reduce an agent’s expected utility through an increase in the stochastic reference point. This means that individuals may prefer stochastically dominated lotteries. In this sense, hope, understood as a small probability of a better outcome, can be a curse. While K?szegi and Rabin focus on a linear specification of the utility function, we show that this effect occurs more broadly. Using fairly plausible assumptions and parameter values, we specify the conditions under which it occurs, as well as the type of lotteries in which this should be expected. We then show that while a simple subjective transformation of probability into weights of the reference point may in some cases mitigate the issue, in others, it can intensify it or even generate new ones. Finally, we extend the model by adding the individual’s current reference point (status quo) to the stochastic reference point. We show that this modification can reconcile K?szegi and Rabin’s model with the apparent empirical infrequency of stochastically dominated choices while maintaining its main qualitative results.     

A Matter of Conscience? The Democratic Significance of 'Conscience Votes' in Legislating Bioethics in Australia

In Australia, members of a political party are expected to vote as a block on the instructions of their party. Occasionally a ‘conscience vote’ (or ‘free vote’) is allowed, which releases parliamentarians from the obligation to maintain party discipline and permits them to vote according to their ‘conscience.’ In recent years Australia has had a number of conscience votes in federal Parliament, many of which have focused on bioethical issues (e.g., euthanasia, abortion, RU486, and embryonic/stem cell research and cloning). This paper examines the use of conscience votes in six key case studies in these contested areas of policy‐making, with particular attention to their implications for promoting democratic values and the significance of women's Parliamentary participation.     

Introduction to the special issue on welfare conditionality in Australia

Conditionality in Australia’s welfare state has sustained a significant academic critique, including the critique published in this journal. In this Special Issue of the Australian Journal of Social Issues, we contribute to the existing critical literature on welfare conditionality. This Special Issue aimed to provide empirical scrutiny into welfare reform and conditionality in Australia. The articles extend our understanding of welfare conditionality’s underpinnings and its lived effects. These case studies illuminate the aspects of welfare conditionality that have not received enough attention: the role of technology, the question of mobility, the relationship with housing and the little thought given to the state’s role in mutual obligation. What is clear is that the individualisation of structural problems is not just a theoretical and political misstep ripe for critique, but leads to the formulation of policies that impact marginalised people’s capacity to shape life on their own terms. Through different empirical foci, all papers in this Special Issue demonstrate how welfare conditionality is put forward as a solution to address the consequences of structural disadvantage.