A method for evaluating the behavior of power indices in weighted plurality games

In this paper, a systematic method to facilitate the comparison of a priori measures of power in an n-player r-candidate (n, r) weighted plurality game is proposed. This method, which exploits the notion of a structure of embedded winning coalitions (SEWC), enables the listing of all power profiles relevant to an (n, r) game under a given index and permits the computation of the probability of occurrence of each of these profiles. The vulnerability of an index to different paradoxes of power can also be systematically studied. For the purpose of illustration, we apply this method to the analysis of four well-known 2-candidate power indices namely the Shapley-Shubik index, the Banzhaf index, the Johnston index and the Deegan-Packel index. In each case, the set of power profiles and the likelihood of occurrence of each of these profiles are enumerated. The superadditivity property of these indices is also studied. Received: 20 October 1999/Accepted: 25 April 2001     

A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy’s (Int J Game Theory 8:133–164, 1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (Social Choice Welfare 18:135–153, 2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy’s paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy’s paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.     

Measuring influence in command games

In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in the command game is a follower of the coalition under the command influence function. Some of the presented influence functions are equivalent to the command games, that is, they are compatible with the command games, and additionally each follower of a coalition under the command influence function is also a commandable player for that coalition in the command games. For some influence functions we define the equivalent command games. We show that not for all influence functions the compatible command games exist. Moreover, we propose a more general definition of the influence index and show that under some assumptions, some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. Both the Shapley–Shubik index and the Banzhaf index are equal to a difference between the weighted influence indices under some influence functions, and the only difference between these two power indices lies in the weights for the influence indices. An example of the Confucian model of society is broadly examined. The authors wish to gratefully thank two anonymous referees for useful suggestions concerning this paper.     

The Chairman’s Paradox Revisited

This paper re-examines the so-called ‘chairman’s paradox‘ that was first noticed by Farquharson in his path breaking tract on sophisticated voting, Theory of Voting (1969). The Chairman’s paradox is concerned with the case of a three member committee in which a particular player who has a regular and a tie-breaking vote – the ‘chairman’ – not only will do worse in specific instances under the plurality procedure for three alternatives than if he did not have such a vote, but will also do worse overall. That is, the chairman’s a priori probability of success (‘getting what one wants’) for all possible games with linear (strict) preference orders is lower than that of the two regular members. It is demonstrated that this result, which comes about if voters act strategically rather than sincerely, is not as robust as it has been thought to be. By merely replacing the standard assumption of linear preference orders with weak preference orders, which allow for indifference, we can escape from the paradox for the canonical case of three players and three alternatives. With weak preference orders, the a priori success of the chairman is now greater than that of the other two players. We also point to a new paradox of sophisticated voting.     

Characterizations of two power indices for voting games with r alternatives

In the first three sections of this paper we present a set of axioms which provide a characterization of an extension of the Banzhaf index to voting games with r alternatives, such as the United Nations Security Council where a nation can vote “yes”, “no”, or “abstain”. The fourth section presents a set of axioms which characterizes a power index based on winning sets instead of pivot sets. Received: 4 April 2000/Accepted: 30 April 2001     

The paradox of multiple elections

Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on a referendum. If the winning combination is NYY on the first, second, and third propositions, respectively, the paradox of multiple elections is that NYY can receive the fewest votes of the 2³ = 8 combinations. Several variants of this paradox are illustrated, and necessary and sufficient conditions for its occurrence, related to the “incoherence” of support, are given. The paradox is shown, via an isomorphism, to be a generalization of the well-known paradox of voting. One real-life example of the paradox involving voting on propositions in California, in which not a single voter voted on the winning side of all the propositions, is given. Several empirical examples of variants of the paradox that manifested themselves in federal elections – one of which led to divided government – and legislative votes in the US House of Representatives, are also analyzed. Possible normative implications of the paradox, such as allowing voters to vote directly for combinations using approval voting or the Borda count, are discussed. Received: 31 July 1996 / Accepted: 1 October 1996     

Augmenting your own reality: student authoring of science-based augmented reality games

Augmented Reality (AR) simulations superimpose a virtual overlay of data and interactions onto a real-world context. The simulation engine at the heart of this technology is built to afford elements of game play that support explorations and learning in students' natural context--their own community and surroundings. In one of the more recent games, TimeLab 2100, players role-play citizens of the early 22nd century when global climate change is out of control. Through AR, they see their community as it might be nearly one hundred years in the future. TimeLab and other similar AR games balance location specificity and portability--they are games that are tied to a location and games that are movable from place to place. Focusing students on developing their own AR games provides the best of both virtual and physical worlds: a more portable solution that deeply connects young people to their own surroundings. A series of initiatives has focused on technical and pedagogical solutions to supporting students authoring their own games.     

The lifestyle paradox: adverse effects of Internet use on self-rated health status

How individuals subjectively rate their health status stands in close relationship with both actual health status and mortality. Previous research has shown that Internet use in general, and online health information seeking in particular, increases self-rated health status. However, this relationship may not always hold true: Albrecht and Devlieger’s [(1999). The disability paradox: high quality of life against all odds. Social Science & Medicine, 48(8), 977–988] disability paradox captures that those with severe health conditions may still perceive their health as very good. This paper introduces the lifestyle paradox as another exception to the generally positive relationship: those without health conditions may still perceive their health as inferior based on general and health-related Internet use. This paper corroborates the lifestyle paradox empirically using quantitative data from the Oxford Internet Surveys connected to the national census through spatial microsimulation, and 43 qualitative interviews conducted with a subsample of the participants from the quantitative strand. A theoretical explanation for this phenomenon is provided based on the concepts of agenda setting and reference groups: the online realm may make lifestyle topics more salient, and provides a variety of opportunities for comparing oneself to others, thereby influencing how people evaluate their own health. Through describing, verifying and explaining the lifestyle paradox, this paper contributes theoretical and empirical insights into the relationship between Internet use and self-rated health status, and thereby adds to the scientific debate around tangible outcomes of Internet use.     

Communication networks and their role in cooperative games

We consider cooperative games subordinated to communication networks, which indicate those players able to communicate directly as well as the strengths of their relationships. We develop an index of a player's ability to communicate with others and we also create a new game whose solution reflects this ability in conjunction with the economic capabilities described by the original game.     

Different least square values,different rankings

The semivalues (as well as the least square values) propose different linear solutions for cooperative games with transferable utility. As a byproduct, they also induce a ranking of the players. So far, no systematic analysis has studied to which extent these rankings could vary for different semivalues. The aim of this paper is to compare the rankings given by different semivalues or least square values for several classes of games. Our main result states that there exist games, possibly superadditive or convex, such that the rankings of the players given by several semivalues are completely different. These results are similar to the ones D. Saari discovered in voting theory: There exist profiles of preferences such that there is no relationship among the rankings of the candidates given by different voting rules. Received: 5 November 2000/Accepted: 12 February 2001     

Paradoxes of Sexuality,Gay Identity,and the Closet

In this project, I illustrate how eight premises of sexuality, gay identity, and the closet contribute to the existence of paradox, an interactional situation constituted by contradiction. I first outline the following premises: gay identity is (1) inextricably tied to the metaphor of the closet; coming out is necessary when gay identity (2) is invisible; the closet draws meaning (3) only in relation to heteronormative contexts; gay identity, as a (4) stigmatized identity, makes coming out a (5) potentially dangerous act; coming out is conceived of as a (6) necessary and important, (7) discrete and linear, (8) inescapable and ever‐present process. I then use autoethnography to describe and analyze the lived experience of paradox in terms of these premises. I conclude by formulating ways a gay person can negotiate paradox in, and by way of, interaction.     

Social Capital and Human Mortality: Explaining the Rural Paradox with County‐Level Mortality Data

The “rural paradox” refers to standardized mortality rates in rural areas that are unexpectedly low in view of well‐known economic and infrastructural disadvantages there. We explore this paradox by incorporating social capital, a promising explanatory factor that has seldom been incorporated into residential mortality research. We do so while being attentive to spatial dependence, a statistical problem often ignored in mortality research. Analyzing data for counties in the contiguous United States, we find that: (1) the rural paradox is confirmed with both metro‐nonmetro and rural‐urban continuum codes, (2) social capital significantly reduces the impacts of residence on mortality after controlling for race and ethnicity and socioeconomic covariates, (3) this attenuation is greater when a spatial perspective is imposed on the analysis, (4) social capital is negatively associated with mortality at the county level, and (5) spatial dependence is strongly in evidence. A spatial approach is necessary in county‐level analyses such as ours to yield unbiased estimates and optimal model fit.     

Acyclic social choice from finite sets

This paper characterizes acyclic preference aggregation rules under various combinations of monotonicity, neutrality, decisiveness, and anonymity, in the spirit of Nakamura's (1979) Theorem on the core of simple games. Each of these characterizations can be seen to follow from Ferejohn and Fishburn's (1979) result on acyclic aggregation rules assuming only independence of irrelevant alternatives. We then state as corollaries to these characterizations extant results such as Sen's (1970) liberal paradox, Blau and Deb's (1977) theorem on the existence of vetoers, and Brown's (1975) theorem on the non-emptiness of the collegium.I thank David Austen-Smith, Michel Le Breton, Maurice Salles, and two anonymous referees for numerous enlightening conversations and comments. I also thank the National Science Foundation and Sloan Foundation for generous financial assistance.     

Perceived harmony,similarity and cooperation in 2 × 2 games: An experimental study

Game harmony is a generic game property describing how conflictual or non-conflictual the interests of players are. Simple and general game harmony measures can predict mean cooperation in 2 × 2 games such as the Prisoner’s Dilemma, the Chicken and trust games. Two measures can be simply computed from monetary payoffs; another, the similarity index, can also be justified by theories of similarity-based reasoning. When data from Oxford and Frankfurt–Oder are disaggregated across experiments, countries and learning history, and when the similarity index is a valid measure, parsimonious regressions can explain around half of the variance in mean cooperation rates.     

Objective Subjectification: The Antimethod of Social Work

This article sets out to understand an important paradox in the author's action research cooperation with a social work development project called "Wild Learning": the fact that the methods developed in the project mostly consist in antimethod. A sketch of the theoretical concepts in the dialectical tradition of method, objectification, subjectification, and participation is presented to explain the idea that social work itself represents a paradoxical form of knowledge, which can be only inadequately and temporarily objectified as method by way of what is introduced as a "boundary objectivity." Current "postmodern" forms of this paradox are briefly considered. As a conclusion, an overall understanding of social work as "critique" is suggested, in which both "method" and "antimethod" are necessary moments in a continuous transformation.     

The apex power measure for directed networks

In this paper we provide an axiomatization of the Shapley value restricted to the class of apex games using an equal loss property which states that the payoff of an apex player and a non-apex player decrease by the same amount if we make this particular non-apex player a null player. We also generalize this axiomatization to the class of games that can be obtained as sums of apex games. After discussing these axiomatizations we apply apex games and their Shapley values in measuring relational power in directed networks. We conclude by mentioning how these results can be adapted to give axiomatizations of the Banzhaf value. Received: 17 February 1999/Accepted: 2 October 2002     

Doing Gender in Academic Education: The Paradox of Visibility

Recent contributions in the field of gender and organization point to the notion of paradox to unveil the persistence of gender inequality in organizations. This article seeks to contribute to this growing body of knowledge. We used the notion of paradox to reveal the processes of doing gender at an earth science department of a Dutch university in order to find out whether gender segregation in academic and professional careers has already started during academic education. We focused on the study choices of female students in earth sciences and discovered the paradox of visibility, which enabled us to show the contradictory and ambiguous nature of how gender is done at this department. In this article we discuss the relationship between doing gender and paradox on a theoretical as well as an empirical level. We argue that paradoxes could be very useful when analysing doing gender in organizations, because paradoxes focus on the social process in which individual agency and social structures come together. We even suggest that paradoxes might help us to disrupt the hierarchical nature of the gender binary, because they allow for a constant reflection on ambiguity and contradictions in theorizing as well as in practice.     

Probabilistic cheap talk

We consider a model in which there is uncertainty over when a one-shot game will be played. We show how a mechanism designer can implement desirable outcomes in certain economic games by manipulating only the probability that the game is played in a given round while leaving all other aspects of the game unchanged. We also show that if there is no discounting, this uncertainty imparts a sequential structure that is almost mathematically equivalent to a repeated version of the game with discounting. In particular, a folk theorem applies to such games. Thus, games of probabilistic cheap provide a third interpretation of the repeated game framework with the additional feature that expected payoff is invariant to the probability of the game ending. Received: 10 May 1999/Accepted: 16 October 2000     

Criticality in games with multiple levels of approval

In this article, criticality within a voting game is rigorously defined and examined. Criticality forms the basis of the traditional voting power measures frequently employed to analyse voting games; therefore understanding criticality is a pre-requisite to understanding any such analysis. The concept of criticality is extended to encompass games in which players are allowed to express multiple levels of approval. This seemingly innocuous extension raises some important questions, forcing us to re-evaluate exactly what it means to be critical. These issues have been largely side-stepped by the main body of research as they focus almost exclusively on ‘yes/no’ voting games, the so called single level approval voting games. The generalisation to multilevel approval voting games is much more than just a theoretical extension, as any single level approval game in which a player can abstain is in effect a multilevel approval voting game.     

Zur Paradoxie der Paradoxie — Diagnose

In this article paradoxon is defined as self contradiction and as self rejection of meaning. It seems useful to keep a clear difference between spontaneous reaction on paradoxon and of formulating the diagnosis ?paradoxon‘ in a specific situation. The difference between ?thinking the paradox‘ and ?coping with a paradox situation‘ is explained; ways of adequate coping are described.