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.     

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.     

The St. Petersburg Paradox at 300

Nicolas Bernoulli’s discovery in 1713 that games of hazard may have infinite expected value, later called the St. Petersburg Paradox, initiated the development of expected utility in the following three centuries. An account of the origin and the solution concepts proposed for the St. Petersburg Paradox is provided. D’Alembert’s ratio test is used for a uniform treatment of the manifestations of the St. Petersburg Paradox and its solution proposals. It is also shown that a St. Petersburg Paradox can be solved or regained by appropriate transformations of the winnings or their utilities on the one hand or the probabilities on the other. This last feature is novel for the analysis of the St. Petersburg Paradox.     

Mean-risk decision analysis

Some decision theorists criticize expected utility decision analysis and propose mean-risk decision analysis as a replacement. They claim that expected utility decision analysis neglects attitudes toward risk whereas mean-risk decision analysis accords these attitudes their proper status. However mean-risk decision analysis and expected utility decision analysis are not incompatible, and it is advantageous for decision theory to develop each in a way that complements the other. Here I present a mean-risk rule that governs preferences among options and options given states. This mean-risk rule complements an expected utility rule that takes the utility of an option-state pair as the utility of the option given the state. I argue for the mean-risk rule using principles concerning basic intrinsic desires. The rule is comparative, but the last section offers some suggestions for its quantitative development.I am grateful for comments from my colleague, Henry E. Kyburg, Jr.     

Newcomb's many problems

Newcomb's paradox rests on two arguments one appealing to the principle of maximizing expected utility and one appealing to dominance in order to generate conflicting recommendations in certain kinds of choice situations. In my essay, I argue that the applications of the principle of maximizing expected utility and of the dominance principle are both fallacious and that the specification of the decision problem is too indeterminate to render a verdict between the two options considered. I also show that if Nozick's case for invoking the dominance principle is taken seriously, it leads to contradictions.     

The chain store paradox

The chain store game is a simple game in extensive form which produces an inconsistency between game theoretical reasoning and plausible human behavior. Well-informed players must be expected to disobey game theoretical recommendations.The chain store paradox throws new light on the well-known difficulties arising in connection with finite repetitions of the prisoners dilemma game. Whereas these difficulties can be resolved by the assumption of secondary utilities arising in the course of playing the game, a similar approach to the chain store paradox is less satisfactory.It is argued that the explanation of the paradox requires a limited rationality view of human decision behavior. For this purpose a three-level theory of decision making is developed, where decisions can be made on different levels of rationality. This theory explains why insight into the rational solution of a decision problem does not necessarily mean that the corresponding course of action will be taken.     

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].     

Mutual Intention

This paper takes as its starting point the problem of characterizing, in a precise way, situations in which two people collaborate to achieve a common goal. It is suggested that collaboration is normally based on an apparently paradoxical state of mind which I call "mutual intention". Mutual intention is a concept belonging to the same family as Lewis's and Schiffer's "mutual knowledge". These concepts have the paradoxical feature that they require, for their definition, an infinite series of propositions of the form X knows (or intends, or assumes) p, where X is a single agent and p is a proposition. The source of these infinite series is traced, and it is shown that they can be represented in a plausible and enlightening way by means of a recursive notation. Finally, three applications of the concept of "mutual intention" are given: (i) in the semantic analysis of certain sentences with plural subjects; (ii) in the analysis of agreement and related speech acts; and (iii) in the clarification of the phenomenon of "implicit agreement".     

Economic policy implications of the Gibson Law in the Netherlands (1800–2012)

Gibson paradox is one of the most discussed economic phenomena in the literature. As observed by Keynes (1930), the most established empirical fact in economics remains unsolved. This paper investigates the Gibson law in the Netherlands over 1800–2012 focusing on the nature of the paradox. Establishing the presence of the paradox outside Gibson (1923) original research in the United Kingdom brings new light to understanding the paradox true nature. A non-linear analysis (logit) is used to identify the factors behind the paradox in the Netherlands. The results provide support that Gibson paradox is the most established empirical fact (non-linear and multivariate) in economics that has pronounced economic policy implications. Policy makers and central banks significantly affect short-term interest rates influencing long-term rates under the expected rise in interest rates for circulation credits. High purchasing power means better micro and macro liquidity and less demand for circulations credits directing Gibson regime-switching behaviour.     

The Donation Paradox for Peremptory Challenges

A donation paradox occurs when a player gives an apparently valuable prerogative to another player, but does better, according to some criterion. Peremptory challenges, used in choosing a American jury, permit each side to veto a certain number of potential jurors. With even a very simple model of jury selection, it is shown that for one side to give a peremptory challenge to the other side may lead to a more favorable jury, an instance of the donation paradox. Both a theorem and examples are given concerning the existence of the donation paradox in the optimal use of peremptory challenges.     

Liberals and information

A resolution of Sen's paretian liberal paradox is provided which does not require agents to waive their rights or have self-supporting preferences. The solution concept is an elaboration of a certain kind of path dependence, primary path construction.     

Resolving Rabin’s paradox

We present a theoretical model of Rabin’s famous calibration paradox that resolves confusions in the literature and that makes it possible to identify the causes of the paradox. Using suitable experimental stimuli, we show that the paradox truly violates expected utility and that it is caused by reference dependence. Rabin already showed that utility curvature alone cannot explain his paradox. We, more strongly, do not find any contribution of utility curvature to the explanation of the paradox. We find no contribution of probability weighting either. We conclude that Rabin’s paradox underscores the importance of reference dependence.

     

Buying and selling price for risky lotteries and expected utility theory with gambling wealth

I analyze two expected utility models which abandon the consequentialist assumption of terminal wealth positions. In the expected utility of gambling wealth model, in which initial wealth is allowed to be small, I show that a large WTA/WTP gap is possible and the (Rabin in Econometrica, 68(5), 1281–1292, 2000) paradox may be resolved. Within the same model the classical preference reversal which allows arbitrage is not possible, whereas preference reversal (involving buying prices in place of selling prices), which does not allow arbitrage, is possible. In the expected utility of wealth changes model, in which there is no initial wealth, I show that both a WTA/WTP gap as well as the classical preference reversal are possible due to loss aversion, both in its general as well as some specific forms.     

How to combine pareto optimality with liberty considerations

I argue that the liberty condition of Sen's important impossibility of a Paretian liberal result is not a condition that liberals (or libertarians) would accept. The problem is that an appropriate liberty condition must be formulated in terms of consent - not in terms of preference. To formulate an adequate condition the framework needs to expand from collective choice rules (which only take information about preferences as input) to rights-based social choice rules (which also take as input information about which options have been consented to and which would violate someone's rights). I formulate a more adequate liberty condition based on the notion of consent that is acceptable to liberals, and then show that Pareto optimality is incompatible even with that condition. I then show how the liberty condition can be weakened in a plausible manner, and describe an interesting class of theories - rights-based Paretian theories - that satisfy the Pareto optimality requirement while being sensitive to liberty considerations.     

Trust, Staking, and Expectations

Trust is a kind of risky reliance on another person. Social scientists have offered two basic accounts of trust: predictive expectation accounts and staking (betting) accounts. Predictive expectation accounts identify trust with a judgment that performance is likely. Staking accounts identify trust with a judgment that reliance on the person's performance is worthwhile. I argue (1) that these two views of trust are different, (2) that the staking account is preferable to the predictive expectation account on grounds of intuitive adequacy and coherence with plausible explanations of action; and (3) that there are counterexamples to both accounts. I then set forward an additional necessary condition on trust (added to the staking view), according to which trust implies a moral expectation. When A trusts B to do x , A ascribes to B an obligation to do x , and holds B to this obligation. This Moral Expectation view throws new light on some of the consequences of misplaced trust. I use the example of physicians' defensive behavior/defensive medicine to illustrate this final point.     

A “Pseudo-endowment” effect,and its implications for some recent nonexpected utility models

This article describes a modification of the Allais paradox that induces preferences inconsistent with two conditions weaker than the independence axiom, namely quasi-convexity (a special case of which is the betweenness axom), and Hypothesis II of Machina (also called fanning-out). These violations can be formally derived from prospect theory by invoking a nonliner transformation of probability into decision weight.I would like to thank David Bell, Vijay Krishna, John Pratt, and especially Colin Camerer for helpful comments and criticism.     

广西县域金融发展的悖论关系研究

通过对广西县域金融的现状研究发现,广西县域金融发展悖论关系主要有县域经济快速发展与县域金融规模收缩相悖,县域企业弱质与金融机构风险控制强化相悖,以及县域资金供给不足与大量信贷资金外流相悖等三个方面。解决这些问题应从发挥政策性金融支持功能,深化农村金融改革,鼓励民营银行进军县域金融市场以及规范民间金融和完善金融生态等方面考虑。     

Barrett and Arntzenius's Infinite Decision Puzzle

The Barrett and Arntzenius (1999) decision paradox involves unbounded wealth, the relationship between period-wise and sequence-wise dominance, and an infinite-period split-minute setting. A version of their paradox involving bounded (in fact, constant) wealth decisions is presented, along with a version involving no decisions at all. The common source of paradox in Barrett–Arntzenius and these other examples is the indeterminacy of their infinite-period split-minute setting.