A Banzhaf share function for cooperative games in coalition structure

A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing properties.     

All for one or one for all? Authorship and the cross-sectoral valuation of credit in nutrition science

The passionate pursuit of authorships is fuelled by the value they represent to scholars and scientists. This article asks how this value differs across scientists and how these different processes of valuation inform authorship articulation, strategies, and publication behavior in general. Drawing from a qualitative analysis of authorship practices among nutrition scientists employed at universities, contract research organizations, and in food industry, I argue that two different modi operandi emerge when it comes to authorship. These different ways of working produce different collaborative approaches, different credit distribution strategies amongst collaborators, and different value placed upon (the pursuit of) authorship. These different valuation processes are neither explicit nor recognizable to those reading (and judging) author lists. As a consequence, in the politics of authorship, the names standing atop a scientific publication in nutrition science represent different types of value to both the individuals and employing organizations.     

Some quantitative concepts of value and utility from a utilitarian point of view

This paper clarifies and interprets some basic quantitative concepts of value, utility and utility function from a utilitarian point of view. First, I discuss the question as to whether value is objective or subjective. I hold that value is subjective and statistical in nature (although from the various subjective values of a certain object a norm can usually be obtained). Second, I emphasize the distinction between use value and exchange value in relation to utility. Third, I propose a law of diminishing incremental interest, which refers to the incremental (marginal) utility of money. Fourth, I identify the utility of money with the von Neumann-Morgenstern utility. Fifth, I question the necessity of the usual normalization of utility functions and the restricted linear transformation (and the consequent concept of strategic equivalence). Sixth, I discuss in detail the terminal values and utilities of a utility function from a philosophical rather than mathematical point of view, particularly the boundedness of a utility function and the magnitudes of V ₀ and U ₀. Finally, I conclude that, in order to be able to have interpersonal comparisons of utility, utility should have the same dimension as value rather than no dimension, and the normalization problem should be reconsidered in the light of terminal values and utilities.     

Constrained egalitarianism in a simple redistributive model

The paper extends a result in Dutta and Ray's (1989) theory of constrained egalitarianism initiated by relying on the concept of proportionate rather than absolute equality. We apply this framework to redistributive systems in which what the individuals get depends on what they receive or pay qua members of generally overlapping groups. We solve the constrained equalization problem for this class of models. The paper ends up comparing our solution with the alternative solution based on the Shapley value, which has been recommended in some distributive applications.     

Analysis of Intertemporal Choice: A New Framework and Experimental Results

This paper reports the results of a series of experiments examining intertemporal choice. The paper makes three contributions: First, it presents a new analytic device, the intertemporal choice triangle, which is analogous to the Marschak--Machina choice triangle used in the analysis of choice under risk. Second, we have developed a new experimental design based on the intertemporal choice triangle which allows subjects greater flexibility in making choices, and which allows the researcher to make more subtle inferences, than are possible with designs previously employed. Subjects are able to create their most-preferred outcome in each choice situation by choosing a constrained linear combination of two extreme options. Third, our results show that while subjects do not typically maximize present value, they are significantly influenced break by present value considerations. We refer to this finding as it present value-seeking behavior. We find only weak evidence of several previously documented intertemporal choice anomalies in our framework.     

The Value of a Statistical Life and the Coefficient of Relative Risk Aversion

Individuals’ risk preferences are estimated and employed in a variety of settings, notably including choices in financial, labor, and product markets. Recent work, especially in financial economics, provides estimates of individuals’ coefficients of relative risk aversion (R’s) in excess of one, and often significantly higher. However, it can be shown that high R’s imply equally high values for the income elasticity of the value of a statistical life. Yet estimates of this elasticity, derived from labor and product markets, are in the range of 0.5 to 0.6. Furthermore, it turns out that even an R below one is difficult to reconcile with these elasticity estimates. Thus, there appears to be an important (additional) anomaly involving individuals’ risk-taking behavior in different market settings.JEL Classification: D80, G11, G12, I10, J17     

Health-health analysis: A new way to evaluate health and safety regulation

Regulations to promote health and safety that are exceptionally costly relative to the expected health benefits may actually worsen health and safety, since compliance reduces other spending, including private spending on health and safety. Past studies relating income and mortality give estimates of the income loss that induces one death — a value that we call willingness-to-spend (WTS)-to be around 9 to9 to 12 million. Such estimates help identify regulations that do not improve health and safety, and moreover, fail benefit-cost comparisons. WTS is a multiple of the willingness to pay to avert a statistical death. International data yield estimates of WTS and willingness-to-pay in different countries.The views of the authors do not necessarily reflect the views of the Office of Information and Regulatory Affairs or OMB. Thanks are due to Ivy Broder, Kenneth S. Chapman, Govind Hariharan, and W. Kip Viscusi for helpful comments. Some of this material is included in theRegulatory Program of the United States Government, April 1, 1992, March 31, 1993, of the Executive Office of the President.     

价值的德育学科分类方法探讨

价值分类反映的是价值主体需要类别和价值客体所能提供需要的某种或多种属性。科学的分类应明确价值内容与价值表现形式的关系,厘清价值内容及其表现形式与价值分类的边界;研究真善美对价值分类的影响。根据主客体需要关系来界定价值本质与内涵,在当前的德育学科建设中,价值分类应主要基于价值主体与价值客体两个角度:从价值主体角度进行分类,体现了价值主体构成的多样性与价值需要的丰富性,可以为进一步研究价值主体提供理论依据。从价值客体的角度进行分类,人作为社会的价值客体,体现的是他的社会价值;作为自己的价值客体,体现的是自我的价值。人与社会、他人和自身的独特价值类型,体现了社会价值与自我价值的辩证统一。     

Valuing Others’ Information under Imperfect Expectations

Sometimes we believe that others receive harmful information. However, Marschak’s value of information framework always assigns non-negative value under expected utility: it starts from the decision maker’s beliefs – and one can never anticipate information’s harmfulness for oneself. The impact of decision makers’ capabilities to process information and of their expectations remains hidden behind the individual and subjective perspective Marschak’s framework assumes. By introducing a second decision maker as a point of reference, this paper introduces a way for evaluating others’ information from a cross-individual, imperfect expectations perspective for agents maximising expected utility. We define the cross-value of information that can become negative – then the information is “harmful” from a cross-individual perspective – and we define (mutual) cost of limited information processing capabilities and imperfect expectations as an opportunity cost from this same point of reference. The simple relationship between these two expected utility-based concepts and Marschak’s framework is shown, and we discuss evaluating short-term reactions of stock market prices to new information as an important domain of valuing others’ information.      

Advocacy Coalitions and Health Politics in Korea

This article analyses the political dynamics underlying health care reform in Korea after the Asian economic crisis. The reform was a significant volte‐face in respect of the social policy paradigm, which now aims to enhance equity in National Health Insurance. The article pays special attention to the evolution of the advocacy coalition for equity in health policy and how it developed the two attributes required for successful policy change: institutional strength and the elaboration of policy rationale for reform. This process was not a simple linear development but a combination of setbacks and advances. The article also takes into consideration the structural conditions that set the policy environment over the course of the advocacy coalition's evolution since the 1960s. In short, the policy reform of 2000 was not a simple policy change in response to the economic crisis, but rather the outcome of the long‐term evolution of the advocacy coalition for equity in health policy.     

A Mixed Methods Examination of Adolescents' Reports of the Values Emphasized in Their Families

Building on value socialization and personal values theories, this study examined adolescents' open‐ended reports of the values their families emphasize. Based on open‐ended reports of an ethnically and socioeconomically diverse sample of adolescents, we described adolescent‐reported familial values using qualitative and cluster analysis techniques. Adolescents' open‐ended responses about the values held by their families were coded using a prominent circumplex value model, and values largely, but not completely, aligned with this model. Using person‐oriented cluster analysis on the coded data, seven distinct value clusters were identified that captured various sets of values that adolescents hear from families. Several demographic differences emerged among the clusters, and mean differences by familial value cluster were found for adolescents' close‐ended reports of values of helping others and religiosity. Results suggest that adolescents are able to articulate values emphasized in their families in ways that fit a universal structure of values; these values are related in meaningful ways to the values that they themselves want to live by.     

价值的科学——韦伯社会科学方法论再探

面对现代社会中理性与非理性、主观与客观、事实与价值之间的紧张,马克斯·韦伯的社会科学方法论力图在对立双方之间搭建起关联并在研究中往复运动,借助包含价值的历史个体和理想类型,通过超越主客观对立的价值阐释,说明历史、文化与社会的各种独特现象,发现各民族和时代中人们的价值理想,理解先辈如何去坚持和实践它们,进而指导现代人在今天继承和实现这些价值。历史和社会科学,既要用理性的方法培养学人清明的理智,也要使人看到超越理性的价值信念,从而帮助人在高度抽象的现代社会中,以理性的态度去守护和坚持各种文明的价值核心,避免走向僵死的理性和狂热的非理性两个极端。     

Olson VS. Coase: Coalitional Worth in Conflict

We analyze a model of conflict with endogenous choice of effort, where subsets of the contenders may force the resolution to be sequential: First the alliance fights it out with the rest and – in case they win – later they fight it out among themselves. For three-player games, we find that it will not be in the interest of any two of them to form an alliance. We obtain this result under two different scenarios: equidistant preferences with varying relative strengths, and varying vicinity of preferences with equal distribution of power. We conclude that the commonly made assumption of super-additive coalitional worth is suspect.     

New Perspectives on the Study of the Authority Relationship: Integrating Individual and Societal Level Research

The concept of authority crosses many social sciences, but there is a lack of common taxonomy and definitions on this topic. The aims of this review are: (1) to define the basic characteristics of the authority relationship, reaching a definition suitable for the different domains of social psychology and social sciences; (2) to bridge the gap between individual and societal levels of explanation concerning the authority relationship, by proposing an interpretation within the framework of social representations. The authority relationship can be conceived as a negotiation of meanings and it is closely linked to shared value orientation and the attribution of meanings negotiated within a society. We assume that the authority relationship is socially constructed and represents both a shared representation of society and a normative principle of social life. A multidisciplinary approach is adopted, crossing definitions and studies provided in sociology, political science, law and social psychology.     

Second-order probabilities and belief functions

A second-order probability Q(P) may be understood as the probability that the true probability of something has the value P. True may be interpreted as the value that would be assigned if certain information were available, including information from reflection, calculation, other people, or ordinary evidence. A rule for combining evidence from two independent sources may be derived, if each source i provides a function Q _i (P). Belief functions of the sort proposed by Shafer (1976) also provide a formula for combining independent evidence, Dempster's rule, and a way of representing ignorance of the sort that makes us unsure about the value of P. Dempster's rule is shown to be at best a special case of the rule derived in connection with second-order probabilities. Belief functions thus represent a restriction of a full Bayesian analysis.     

社会科学、价值判断与科学的价值——评施特劳斯的韦伯论述

在施特劳斯的思想世界中，韦伯的处境是悲剧性的：他命定了要信仰科学，可是由于受到历史主义的深刻影响，内心深处又不得不对科学的价值怀有极度的不安。施特劳斯一方面通过一个下降的思想历程揭示出韦伯困境的深层根源：韦伯坚持价值中立是因为终极价值之间的冲突无法借助理性来解决，而后者又是因为科学无法在面临启示的挑战之下证明自身的价值，这是因为他对科学及其处境的理解是不完善的。另一方面，施特劳斯又通过一个上升的思想历程去超越韦伯所陷入的深渊：前哲学的自然世界是哲学与启示的共同起点，通过政治哲学（必然要求价值判断）迈向一种探询式怀疑主义的哲学，它始终满足于表述而非解决存在之谜，这就使得启示成为可能和必要。哲学的价值在这种永恒冲突中得到确立。     

马克思主义公正观的基本向度及方法论原则(英文)

在社会公正问题的大讨论中,罗尔斯、诺齐克、哈耶克、麦金泰尔等当代西方思想家的论述被反复引用和申说,而将马克思恩格斯等经典作家的观点置于一种被忽视甚至被忘却的状态。形成这种状态的原因是多方面的。对历史背景和语境不作具体的分析,就难以把握马克思恩格斯对于社会公正问题的真实态度和精神实质,甚至会得出他们不仅没有关于社会公正的理论,而且反对和拒斥从社会公正角度讨论问题的结论。马克思主义作为无产阶级认识和改造世界、求得自身解放和人类解放的世界观和方法论,是真理与价值相统一的理论,也只有从科学向度与价值向度辩证统一的角度,才可能对作为价值之一种表现的公正问题作出合理的理解。公正既是一种价值观念,具有评价标准的功能,也是实际的价值（包括利益、机会、权利等）分配的一种状态,其中会涉及自由与平等的矛盾、形式公正与实质公正的矛盾、一般与特殊的差别、平等与效率的抵牾、公正与不公正的对立,等等,只有运用辩证思维的方法,才能对其复杂性获得正确的认识。     

On Myopic Stability Concepts for Hedonic Games

We present a unified look at myopic stability concepts for hedonic games, and discuss the status of the existence problems of stable coalition structures. In particular, we show that contractual strictly core stable coalition structures always exist, and present a sufficient condition for the existence of contractually Nash stable coalition structures on the class of separable games. We gratefully acknowledge financial support from the Alexander von Humboldt Foundation (D. Dimitrov)“by “D. Dimitrov gratefully acknowledges financial support from the Alexander von Humboldt Foundation.     

Axiomatization of a class of share functions for n-person games

The Shapley value is the unique value defined on the class of cooperative games in characteristic function form which satisfies certain intuitively reasonable axioms. Alternatively, the Banzhaf value is the unique value satisfying a different set of axioms. The main drawback of the latter value is that it does not satisfy the efficiency axiom, so that the sum of the values assigned to the players does not need to be equal to the worth of the grand coalition. By definition, the normalized Banzhaf value satisfies the efficiency axiom, but not the usual axiom of additivity.In this paper we generalize the axiom of additivity by introducing a positive real valued function on the class of cooperative games in characteristic function form. The so-called axiom of -additivity generalizes the classical axiom of additivity by putting the weight (v) on the value of the gamev . We show that any additive function determines a unique share function satisfying the axioms of efficient shares, null player property, symmetry and -additivity on the subclass of games on which is positive and which contains all positively scaled unanimity games. The axiom of efficient shares means that the sum of the values equals one. Hence the share function gives the shares of the players in the worth of the grand coalition. The corresponding value function is obtained by multiplying the shares with the worth of the grand coalition. By defining the function appropiately we get the share functions corresponding to the Shapley value and the Banzhaf value. So, for both values we have that the corresponding share functions belong to this class of share functions. Moreover, it shows that our approach provides an axiomatization of the normalized Banzhaf value. We also discuss some other choices of the function and the corresponding share functions. Furthermore we consider the axiomatization on the subclass of monotone simple games.     

Comparative accuracy of value solutions in non-sidepayment games with empty core

This article reports a test of the predictive accuracy of solution concepts in cooperative non-sidepayment n-person games with empty core. Six solutions were tested. Three of these were value solutions (i.e., -transfer value, -transfer nucleolus, and -transfer disruption value) and three were equilibrium solutions (deterrence set, stable set, and imputation set). The test was based on a laboratory experiment utilizing 5-person, 2-choice normal form games with empty core; other related data sets were also analyzed. Goodness-of-fit results based on discrepancy scores show that the three value solutions are about equally accurate in predicting outcomes, and that all three are substantially more accurate than the other solutions tested.