Perspectives on a Pair of Envelopes

The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue).     

Utility theory and the Bayesian paradigm

In this paper, a problem for utility theory - that it would have an agent who was compelled to play Russian Roulette with one revolver or another, to pay as much to have a six-shooter with four bullets relieved of one bullet before playing with it, as he would be willing to pay to have a six-shooter with two bullets emptied - is reviewed. A less demanding Bayesian theory is described, that would have an agent maximize expected values of possible total consequence of his actions. And utility theory is located within that theory as valid for agents who satisfy certain formal conditions, that is, for agents who are, in terms of that more general theory, indifferent to certain dimensions of risk. Raiffa- and Savage-style arguments for its more general validity are then resisted. Addenda are concerned with implications for game theory, and relations between utilities and values.     

Measuring social trust and trusting the measure

Decades of rigorous quantitative scholarship have generated a wealth of knowledge regarding the causes and consequences of crossnational variations in social trust. However, while some social science disciplines have made significant contributions to this conversation, others have largely failed to do so. The field of international relations, for example, has lagged behind in producing aggregate-level scholarship on social trust. This is surprising given that (1) trust influences public opinion and thereby the incentive structure for political leaders and (2) many peacebuilding efforts directly target the levels of trust in post-conflict settings. Country-level trust scholarship in international relations and the social sciences more generally is hampered by data scarcity. The main purpose of this article is to present a new publicly available data set on aggregate levels of social trust. Relying on a set of 19 widely accepted correlates, we construct a new cross-sectional measure of the concept that covers all countries from 1946 to 2010. We then perform a series of empirical tests establishing the validity of our measure. Finally, we offer a number of bivariate analyses to demonstrate the broad utility of our new variable for scholars in the social sciences.     

Foundations of the theory of evidence: Resolving conflict among schemata

Schematic conflict occurs when evidence is interpreted in different ways (for example, by different people, who have learned to approach the given evidence with different schemata). Such conflicts are resolved either by weighting some schemata more heavily than others, or by finding common-ground inferences for several schemata, or by a combination of these two processes. Belief functions, interpreted as representations of evidence strength, provide a natural model for weighting schemata, and can be utilized in several distinct ways to compute common-ground inferences. In two examples, different computations seem to be required for reasonable common-ground inference. In the first, competing scientific theories produce distinct, logically independent inferences based on the same data. In this example, the simple product of the competing belief functions is a plausible evaluation of common ground. In the second example (sensitivity analysis), the conflict is among alternative statistical assumptions. Here, a product of belief functions will not do, but the upper envelope of normalized likelihood functions provides a reasonable definition of common ground. Different inference contexts thus seem to require different methods of conflict resolution. A class of such methods is described, and one characteristic property of this class is proved.     

Bayesian boundedly rational agents play the Finitely Repeated Prisoner's Dilemma

In this paper a model of boundedly rational decision making in the Finitely Repeated Prisoner's Dilemma is proposed in which: (1) each player is Bayesianrational; (2) this is common knowledge; (3) players are constrained by limited state spaces (their Bayesian minds) in processing (1) and (2). Under these circumstances, we show that cooperative behavior may arise as an individually optimal response, except for the latter part of the game. Indeed, such behaviorwill necessarily obtain in long enough games if belief systems satisfy a natural condition: essentially, that all events consistent with the players' analysis of the game be attributed by them positive (although arbitrarily small) subjective probability.     

道德统计学的社会观:塔尔德与涂尔干之争再考察

鲜有人考察19世纪法国的两位重要社会学家塔尔德和涂尔干之间的争论。本文以两人都倚重的统计学方法为切入口,深入考察两人论辩的实质问题,并力图呈现论辩背后的社会观差异以及各自对社会秩序之基础的思考。塔尔德试图以客观概率的方式去捕捉作为主观变量的社会秩序的生成过程,涂尔干则秉承以凯特莱为代表的道德统计学传统,试图通过纯粹客观的统计数据来捕捉具体社会结构及其功能的正常状态。通过对两人统计学基础的不断追索,本文认为,两人的实质差异在于：塔尔德试图超越社会本体论思考,用单子论的方式把握和理解现代社会特征和秩序的基础,而涂尔干仍然从社会本体的角度做社会学式思考,探寻现代社会的秩序基础。     

A Bayesian examination of information and uncertainty in contingent valuation

A theoretical framework is presented to explain how agents respond to information under uncertainty in contingent valuation surveys. Agents are provided with information signals and referendum prices as part of the elicitation process. Agents use Bayesian updating to revise prior distributions. An information prompt is presented to reduce hypothetical bias. However, we show the interaction between anchoring and the information prompt creates a systematic bias in willingness to pay. We test our hypotheses in an experimental setting where agents are asked to make a hypothetical, voluntary contribution to a public good. Experimental results are consistent with the model.

Biting the Bayesian bullet: Zeckhauser's problem

A troubling challenge to the basic principles of Bayesian decision theory is analyzed as a case where irrationality is no intellectual flaw but a characterological one, i.e., not stupidity but funk.     

Axiomatic characterizations of solutions for Bayesian games

Bayesian equilibria are characterized by means of consistency and one-person rationality in combination with non-emptiness or converse consistency. Moreover, strong and coalition-proof Bayesian equilibria of extended Bayesian games are introduced and it is seen that these notions can be characterized by means of consistency, one-person rationality, a version of Pareto optimality and a modification of converse consistency. It is shown that, in case of the strong Bayesian equilibrium correspondence, converse consistency can be replaced by non-emptiness. As examples we treat Bayesian potential games and Bayesian congestion games.     

Statistics,ethics, and research: An agenda for education and reform

This essay argues that the research community needs to pay more attention to the appropriate use of statistical methods in discussions of research ethics, and proposes some strategies for enhancing discussions of the ethical uses of statistics within investigational, educational, and organizational settings. The essay supports its position by 1) explaining why statistics plays such a key role in research integrity, 2) describing how some common misuses of statistics in research violate ethical standards pertaining to honesty and error avoidance, and 3) reviewing evidence which suggests that the misuse of statistics is more prevalent (and perhaps more significant) than research misconduct (narrowly defined as “fabrication, falsification, or plagiarism").     

我国财政统计核算改革的目标模式与推进机制

国际货币基金设计的GFS(2001),是目前世界各国较为流行且广泛认可的新型财政统计体系。该体系采用了权责发生制,拓展了核算对象,重新定义和整合政府财政收支体系,相对于GFS(1986),具有巨大的进步。我国应全面借鉴GFS(2001),重新界定广义政府范围,建立以权责发生制为基础的价值确认系统,完整记录政府财政活动、财政资源的基础信息,并进行部门间、政府间相关的数据合并,形成符合我国实际情况、并与国际接轨的政府财政统计核算体系。     

Estimation of a Bernouilli parameter: A normative approach to replace the Bayesian one

The paper deals with the problem of the estimation of an unknown probability from a finite number of experiments. We propose a normative (axiomatic) solution that restricts the class of admissible estimators to a one-parameter family. Moreover this solution coincides with the one obtained from Bayes theory with a prior. Thus our results can be interpreted as a justification for the use of Bayesian inference with a prior.     

A foundation of Bayesian statistics (How to deal with fears)

A rational statistical decision maker whose preferences satisfy Savage's axioms will minimize a Bayesian risk function: the expectation with respect to a revealed (or subjective) probability distribution of a loss (or negative utility) function over the consequences of the statistical decision problem. However, the nice expected utility form of the Bayesian risk criterion is nothing but a representation of special preferences. The subjective probability is defined together with the utility (or loss) function and it is not possible, in general, to use a given loss function - say a quadratic loss - and to elicit independently a subjective distribution.I construct the Bayesian risk criterion with a set of five axioms, each with a simple mathematical implication. This construction clearly shows that the subjective probability that is revealed by a decider's preferences is nothing but a (Radon) measure equivalent to a linear functional (the criterion). The functions on which the criterion operates are expected utilities in the von Neumann-Morgenstern sense. It then becomes clear that the subjective distribution cannot be eliciteda priori, independently of the utility function on consequences.However, if one considers a statistical decision problem by itself, losses, defined by a given loss function, become the consequences of the decisions. It can be imagined that experienced statisticians are used to dealing with different losses and are able to compare them (i.e. have preferences, or fears over a set of possible losses). Using suitable axioms over these preferences, one can represent them by a (linear) criterion: this criterion is the expectation of losses with respect to a (revealed) distribution. It must be noted that such a distribution is a measure and need not be a probability distribution.     

试析人工神经网络运用于社会统计分析中的可能性

社会统计分析是社会研究方法中十分重要的一部分,因为定量研究所得的原始资料在经过审核、整理与汇总之后,需要进行科学系统的统计分析,才能揭示出研究资料所包含的众多信息,从而得出研究的结论。在多元统计分析方法中,研究者用得比较多的是多元线性回归分析、方差分析、log线性模型、probit模型及logistic回归分析,这些分析方法能够帮助我们对数据进行简化、对变量之间的相互依赖关系进行分析,以及根据模型进行预测。但上述方法也存在着一定的使用局限性,比如,方差分析法要假定进行均值比较的总体具有相同的方差和服从正态分布,如果不符合…     

Individual and group decision making under risk: An experimental study of Bayesian updating and violations of first-order stochastic dominance

This paper reports the results of experiments designed to test whether individuals and groups abide by monotonicity with respect to first-order stochastic dominance and Bayesian updating when making decisions under risk. The results indicate a significant number of violations of both principles. The violation rate when groups make decisions is substantially lower, and decreasing with group size, suggesting that social interaction improves the decision-making process. Greater transparency of the decision task reduces the violation rate, suggesting that these violations are due to judgment errors rather than the preference structure. In one treatment, however, less complex decisions result in a higher error rates.

Semantic Analysis of the Theoretical Foundations of Biology

生物学理论作为科学哲学研究中的一个另类一直受到关注。它与传统科学模式间的差异是造成这种现象的原因之一。解读这种差异的根源,需要对生物学的理论基础以及理论结构给予充分的关注。生物学特有理论结构所表现出的多元语境与语义结构的复杂性,决定了对生物学理论基础的研究应当重视语义分析的方法,尤其是对理论本身进行语义分解并研究其中的语义关联问题,从而解读生物学模式作为一种不同于理化科学的特殊科学解释观的合理性。     

Semantic Analysis of the Theoretical Foundations of Biology

生物学理论作为科学哲学研究中的一个另类一直受到关注。它与传统科学模式间 的差异是造成这种现象的原因之一。解读这种差异的根源,需要对生物学的理论基础 以及理论结构给予充分的关注。生物学特有理论结构所表现出的多元语境与语义结构 的复杂性,决定了对生物学理论基础的研究应当重视语义分析的方法,尤其是对理论 本身进行语义分解并研究其中的语义关联问题,从而解读生物学模式作为一种不同于 理化科学的特殊科学解释观的合理性。

关键词: 生物学理论?语义分析?语义结构

As a different type of research in the philosophy of science, biological theory has always attracted scholarly attention. One reason for this phenomenon is that it differs from the traditional scientific paradigm. To explore the root of this difference, we need to examine closely the theoretical foundations and structure of biology. The complexity of the multiple contexts and semantic structures expressed in the theoretical structure specific to biology requires that research on the theoretical foundation of biology incorporate semantic analysis. It is particularly necessary to conduct semantic decomposition of the theories themselves and study their semantic correlations. In doing so, we can discern the rationality of the biological model as a special form of scientific explanation distinct from that of physics and chemistry.     

Constraints and the Measurement of Freedom of Choice

This paper introduces considerations about constraints in the construction of measures of an agent's freedom. It starts with motivating the exercise from both the philosophical and the informational point of view. Then it presents two rankings of opportunity sets based on information about the extent of options and the constraints that a decision maker faces. The first ranking measures freedom as variety of choice; the second as non-restrictedness in choice.