Coalition Configurations and the Banzhaf Index

In this paper, we suppose that players join in coalitions and form a coalition configuration, and we provide a generalization of the normalized Banzhaf-Coleman (1965, 1971) index to this framework.     

The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent

This paper discusses a numerical scheme for computing the Banzhaf swing probability when votes are neither equiprobable nor independent. Examples indicate a substantial bias in the Banzhaf measure of voting power if neither assumption is met. The analytical part derives the exact magnitude of the bias due to the common probability of an affirmative vote deviating from one half and due to common correlation in unweighted simple-majority games. The former bias is polynomial, the latter is linear. A modified square-root rule for two-tier voting systems that takes into account both the homogeneity and the size of constituencies is also provided.     

Axiomatizations of the normalized Banzhaf value and the Shapley value

A cooperative game with transferable utilities– or simply a TU-game – describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways. An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the `grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the `grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms. Received: 10 April 1996 / Accepted: 2 June 1997     

The traveling group problem

This paper combines social choice theory with mathematical optimization by applying various group decision concepts to a classical problem of combinatorial optimization, namely the famous traveling salesperson (salesman) problem. The aim of the latter is to find a tour through all vertices of a given graph along edges of minimal total cost. In this contribution we replace the measure of additive edge costs by the social acceptance of different edges and the resulting tours. In particular, for four different voting rules, the Borda rule, Approval voting, Plurality rule and Simple Majority rule, we will investigate the social acceptance of tours derived from global and local decisions. It will be shown that these two decision approaches can lead to widely varying results.     

The problem of early English sociology

A brief survey is attempted of the recent literature relating to the ‘problem’ of early English sociology, i.e. its apparent failure to produce in the late nineteenth and early twentieth centuries a body of thought comparable to the ‘classical’ sociological tradition which emerged in France and Germany during the same period. It is argued that the absence of such a tradition in England cannot be linked to the supposed failure of the English middle class to develop a corporate identity, as certain contemporary Marxist theorists have suggested. If the continental ‘classical’ tradition reflects the ideology of any social stratum, it is that of the educated middle class, linked to the central state apparatus, which developed in a number of European countries during the nineteenth century. The failure of such an intelligentsia to emerge in England in the same period is reflected in the specific development of English social thought.     

The distribution problem and Rawlsian reasoning

The difference principle of Rawls has been wrongly translated in the formal literature on welfare economics and social choice theory. The difference principle is concerned with the welfare of the members of the least advantaged segment, and, thus, does not – as frequently argued – assign dictatorial power to the person in the worst off position in society. This distinction is important, and the focus on a leximingroup rule makes the Rawlsian position more plausible than it is in the `disguise' of the conventional leximin rule. However, there is a difficulty with this approach, to wit how to understand the least advantaged segment in society. Various definitions are considered in the paper, but it turns out that in most cases these definitions imply that we have to accept the leximin rule. We suggest one line of reasoning that makes the Rawlsian leximingroup rule a genuine alternative to the leximin rule. In this approach, an independent norm level is imposed on the analysis (i.e. a cut off line that is independent of the distribution of welfare under consideration), and the least advantaged segment is identified as those who have less than this minimum stipend. Received: 21 December 1994/Accepted: 15 June 1998     

The division problem with voluntary participation

The division problem consists of allocating a given amount of a homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this article we consider the division problem when agents’ participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents’ shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents’ voluntary participation.     

The social sciences and the population problem

Four essentially independent conceptions of the population problem are visible in current discussions. One is derived from macroeconomics, one from microeconomics, one from the health sciences, and one from ethical concerns about the just relation between man and nature. After describing these conceptions, this paper addresses the population problem principally using the economic definitions. It cites five reasons why discussions of the economic hazards posed by population growth have become markedly less alarmist in the past decade. Failures of highly quantified input-output models to account for human progress are emphasized. The paper presents examples of how technical demography has shed light on the dimensions of and solutions to the population problem and concludes with a brief discussion of contemporary population problems in the U.S.The real world consists not of numbers but of shapes and sizes. It is topological rather than quantitative. Quantification for the most part is a prosthetic device of the human mind, though certainly a very useful one. Anyone who thinks that numbers constitute the real world, however, is under an illusion, and this is an illusion that is by no means uncommon (Boulding, 1980:833).     

The problem of justification in social work

Abstract

In this paper we argue that the real test of professional social work practice is whether it can be plausibly, effectively and defensibly justified. Since the early 1950s social work in Australia has engaged in a strategy of professionalisation. This strategy and its implications were described by McDonald and Jones in 2000. This paper supports the concerns expressed. We argue that the way out of our profession's dilemma is by focusing on the problem of justification. The main questions addressed by McDonald and Jones appear to be: What is professional social work practice? Does the concept of professionalism serve us and our clients well now? What form should social work take in the future? Their answer is ‘that the “strategy of professionalisation”, as conventionally conceived by Australian social work, is no longer viable in the emerging milieu.’ We build on that answer by exploring the notion of justification in terms of the concepts Foundationalism, Coherentism and Reliabilism. We conclude by suggesting that the immediate task for social work in this new century is to solve the problem of justification.