On the structure of minimal winning coalitions in simple voting games

According to Coleman’s index of collective power, a decision rule that generates a larger number of winning coalitions imparts the collectivity a higher a priori power to act. By the virtue of the monotonicity conditions, a decision rule is totally characterized by the set of minimal winning coalitions. In this paper, we investigate the structure of the families of minimal winning coalitions corresponding to maximal and proper simple voting games (SVG). We show that if the proper and maximal SVG is swap robust and all the minimal winning coalitions are of the same size, then the SVG is a specific (up to an isomorphism) system. We also provide examples of proper SVGs to show that the number of winning coalitions is not monotone with respect to the intuitively appealing system parameters like the number of blockers, number of non-dummies or the size of the minimal blocking set.     

On hierarchies and communication

Many economic and political organizations have some relational structure, meaning that participating agents do not only differ with respect to certain individual characteristics such as wealth and preferences, but also belong to some relational structure in which they usually take different positions. Two examples of such structures are communication networks and hierarchies. In the literature, the distinction between these two types of relational structures is not always clear. In models of restricted cooperation, this distinction should be defined by properties of the set of feasible coalitions. We characterize the sets of feasible coalitions in communication networks and compare them with sets of feasible coalitions arising from hierarchies.     

Diverse social movement coalitions: Prospects and challenges

Coalitions are among the most important tactical tools available for social movements and civil resistance campaigns, as they enable the sharing of networks, resources, expertise, and information, while simultaneously projecting an image of power through unity and numbers. Though exceptionally challenging to build, diverse coalitions are viewed by many as particularly important. However, there is considerably less literature that explicitly discusses them. In this article, I review the literature on diverse coalitions, with a focus on both their theorized and documented importance for social movements and civil resistance campaigns, and the challenges they face (including the factors working against their formation and sustainability). To do so, I bring two closely related but often separate literatures into conversation: social movements and civil resistance. I conclude by evaluating the state of this research area, highlighting remaining gaps, and suggesting directions for future research.     

Acyclicity and the dispersion of the veto power

Blair and Pollak (Econometrica (1982) 50: 931–943) prove that, if there are more alternatives than individuals, then, for every arrovian binary decision rule that is acyclic, there is at least one individual who has a veto power over a critical number of pairs of alternatives. If the number of individuals is larger than the number of alternatives, there need not be single vetoers but there could be small coalitions endowed with a similar power. Kelsey (Soc Choice Welfare (1985) 2: 131–137) states precise results in this respect. In this paper, we first give a new and much simpler proof of the main result of Blair and Pollak and complete proofs of the generalization of this result by Kelsey. Then we give a precise answer as to the minimum size of the coalitions that must have a veto power under any acyclic binary decision rule and the minimum number of pairs of alternatives on which these coalitions may exercise their power. We also show that, if the veto power of the coalitions of the minimal size attainable under the last objective is limited to the minimum number of pairs of alternatives, then all larger coalitions have a veto power on all pairs. All the results are obtained by appealing to an acyclicity condition found by Ferejohn and Fishburn (J Econ Theory (1979) 21: 28–45). In the case of symmetric and monotonic binary decision rules, proofs are even easier and illustrate clearly the reasons for the veto power.     

Polyhedral dynamics and conflict mobilization in social networks

A representation of social networks in terms of polyhedral dynamics is used to study the mobilization of individuals in a specific social network. By making use of the distinction between backcloth and traffic, the analysis shows there are compelling structural reasons for the outcome of the mobilization process in the particular network studied.     

In the office: Networks and coalitions

The study of the internal politics of an office demonstrates that levelling coalitions derive from established networks. This contradicts the view that network analysis is not useful in the study of levelling coalitions. Sixteen months of observation of office politics, particularly the functioning of levelling coalitions in the informal structure, could not be understood apart from the social networks from which they had sprung. Recruitment to and participation in the levelling coalitions derives directly from the existing networks. The analysis also demonstrates that the success or failure of the levelling coalition is dependent upon the relationships held and manipulated by the target. In order to understand the conflicts and be able to predict their outcome coalitions and networks must be analyzed.     

The Effects of Different Group Sex Compositions on Support Rates and Coalition Formation

Une réplique des expériences de T. M. Mills sur des coalitions dans les triades, en variant la composition par sexe du groupe, met en lumière le fait que les femmes apportent un meilleur appui que les hommes, qu'elles établissent un plus grand nombre de coalitions et répartissent leur appui de f aeon plus équitable parmi les autres membres lorsqu'elles entrent en interaction avec des personnes de meme sexe. Tandis que le membre le plus inactif de la triade masculine devient un isole, le moins actif de la triade féminine regoit le meilleur appui émotif. Le modele de coalition typique dans la triade masculine est une coalition de deux membres et un isolé: dans le groupe féminin les trois membres du groupe etablissent des coalitions. Dans les triades mixtes, l'impact de l'interaction des membres d'un sexe avec ceux du sexe opposé est de faconner leurs comportements à l'image de ceux des autres. On suggère que le processus qui influence la constitution de coalitions dans les triades mixtes est reliéà la concurrence que se livrent les deux membres du meme sexe pour obtenir l'appui du membre du sexe opposé. Dans une telle situation il n'est pas rare de constater que le membre du sexe minoritaire devient un mediateur entre les deux membres majoritaires du sexe opposé. II s'ensuit une formation de deux coalitions composée du membre minoritaire et d'un membre majoritaire et parfois, des coalitions entre les trois membres du groupe. A replication of T. M. Mills' experiments dealing with coalition-formation in triads, varying the sex composition of the group, reveals that females are more supportive, form more coalitions and distribute their support more equally among others when interacting with members of the same sex, than males do. While the least active member of the triad becomes an isolate in the 3-male groups, the least active member in 3-female groups receives more support than any other group member. The typical coalition pattern in the 3-male groups is a coalition between two, with the third being an isolate: in the 3-female groups, coalitions develop between all three members of the group. In the mixed-sex groups, the effect of interacting with members of the opposite sex on both men and women is to make their behaviour more like the other's. It is suggested that the process that governs the formation of coalitions in mixed-sex triads is that of competition between the two majority-sex members for the support of the one member of the other sex, which often leads to the minority-sex member mediating between the competing pair of the opposite sex, and this results in the formation of two coalitions between the minority-sex member and each of the majority-sex members in the group, and sometimes even in the eventual establishment of coalitions between all three members of the group.     

Special interest group coalitions: Ethical standards for broad-based support efforts

Coalitions are an increasingly important tool of special interest group public affairs efforts. While coalitions are not usually formed with the intent to deceive, some groups take shortcuts which amount to buying results and manipulating the public. These “front” groups which deceive or mislead the public or policy-making bodies can undermine the professionalism of public relations and damage the public trust.The author examines case studies of coalitions formed by a for-profit corporation, a trade association and a foreign government. Findings were that: (1) coalitions perform an important role if they represent a broad public interest but if they do not represent a broad base, they may be deceptive, unethical, and potentially damaging to the public interest; (2) media play an important role as diligent watchdogs but don't always rise to this responsibility, and (3) the public relations profession bears the brunt of public and media concern over unethical coalition activity. Ethical guidelines for coalition development are offered.     

Minimal winning coalitions in weighted-majority voting games

Riker's size principle for n-person zero-sum games predicts that winning coalitions that form will be minimal in that any player's defection will negate the coalition's winning status. Brams and Fishburn (1995) applied Riker's principle to weighted-majority voting games in which players have voting weights w ₁≥w ₂≥...≥w _n,and a coalition is winning if its members' weights sum to more than half the total weight. We showed that players' bargaining power tends to decrease as their weights decrease when minimal winning coalitions obtain, but that the opposite trend occurs when the minimal winning coalitions that form are “weight-minimal”, referred to as least winning coalitions. In such coalitions, large size may be more harmful than helpful. The present paper extends and refines our earlier analysis by providing mathematical foundations for minimal and least winning coalitions, developing new data to examine relationships between voting weight and voting power, and applying more sophisticated measures of power to these data. We identify all sets of minimal and least winning coalitions that arise from different voting weights for n≤6 and characterize all coalitions that are minimal winning and least winning for every n. While our new analysis supports our earlier findings, it also indicates there to be less negative correlation between voting weight and voting power when least winning coalitions form. In this context, players' powers are fairly insensitive to their voting weights, so being large or small is not particularly important for inclusion in a least winning coalition.     

Completeness and Accuracy of Recall in the Diffusion of the News From a Newspaper vs. a Television Source

The study of the word-of-mouth flow of news to audiences is an important if somewhat neglected topic. First, this may be the only means by which some citizens receive information about events and issues in their community. Second, in disaster situations many people cannot be reached by conventional means, and critical information comes to them by word-of-mouth. The present experiment makes use of the Allport and Postman design for the study of the changes (leveling and sharpening) that messages undergo as they are passed from one person to another in serial retelling. A news story of just over 300 words was presented to a set of "starter" subjects. Each then passed on the information to another subject, who in turn passed it on to a third, and so on. Seven such chains were developed with six subjects in each of two versions of the experiment. In one the information was presented as a newspaper story. In the other, the (same) story was presented via television. Those in the newspaper chains remembered more details overall than those involved in the television version. However, a clear pattern of "leveling" was characteristic of all the chains. An analysis of the salient details that survived through the six subjects in each of the chains (regardless of medium) showed a coherent and more or less logical organization of the central ideas and not a random jumble of distorted facts. Thus, word-of-mouth transmission of news can convey meaningful, if greatly abbreviated, versions of stories to a secondary audience. However, the data suggest that audiences recall more complete information from a newspaper presentation of a story than from a television exposure.     

The structure of continuous-valued neutral monotonic social functions

This article consists of several results characterizing neutral monotonic social functions over alternative sets that are compact, convex subsets of Euclidean space. One major result is that a neutral monotonic social function is continuous-valued (i.e., does not make abrupt reversals) for all profiles of continuous-valued weak orderings if and only if it is simple (i.e., completely determined by a single set of decisive coalitions). A second major result is that a continuous-valued neutral monotonic social function will guarantee the existence of a socially undominated alternative for all profiles of continuousvalued, almost convex weak orderings if and only if the smallest empty intersection within the set of decisive coalitions is at least m+2 in size where m is the dimension of the alternative set.Associate Professor of Law, University of Southern California and Assistant Professor of Law and Economics, California Institute of Technology.This article is taken almost directly from a chapter of my Ph.D. dissertation (Strnad 1982). That chapter itself is substantially the same as an earlier paper, Strnad (1981). I have profited greatly from the suggestions, guidance and encouragement of Donald Brown in this work. Strnad (1981) was presented at the California Institute of Technology Theory Workshop in January 1982 and at the annual Public Choice Society Meetings in San Antonio, Texas on March 5–7, 1982. I am grateful to participants at both the Workshop and the Meetings for their comments. Comments by the referee and by Jerry Kramer, the editor, also were very helpful. Any remaining errors are solely my responsibility.Substantial financial support for this work has been provided by Summer Research Grants for 1981 and 1982 from the University of Southern California Law Center     

Social movement coalitions: Formation,longevity, and success

Social movements rely on coalitions to help mobilize the mass numbers of people necessary for success. In this article, we review the literature on social movement coalition formation, longevity, and success. We identify five factors critical to coalition formation: (a) social ties; (b) conducive organizational structures; (c) ideology, culture, and identity; (d) the institutional environment; and (e) resources. Next, we explore the extent to which coalition survival is influenced by these same factors and argue that emergent properties of the coalition, such as commitment and trust, also facilitate longevity. Our review of the literature reveals that two factors specific to coalitions influence their success: coalition form and the nature of institutional targets. Interaction, communication technology, and the availability of physical and virtual spaces that facilitate communication are themes that run throughout our discussion, as they undergird many of the elements that shape coalition formation and survival. We conclude by evaluating the state of the research area and suggesting directions for further research.     

LOGROLLING IN THE U.S. CONGRESS

Does exchange, i.e., vote trading, occur in legislatures?!f so, is it quantitatively important or optimal? How important are political parties for the organization of logrolling coalitions? To address these questions, this paper investigates a broad range of votes where logrolling has been reported among interests favoring subsidies for urban, labor, and farm interests. The findings suggest that logrolling agreements are widespread, that many Democratic congressmen changed votes because of logrolling agreements, and that the Democratic party served to facilitate logrolling between its members. Furthermore, logrolling coalitions exhibited a strong degree if stability.     

Issues and place: the hyperlink network of homeowner forums and implications for collective action

This paper explores the structure and the mechanisms involved in the formation of a hyperlink network of Guangzhou city's 118 homeowner forums in the context of a collective action by the homeowners. It develops a contextual analytical framework contending that the structure of the hyperlink network is influenced by utility values and utilization capability, as well as the media and social environments that shape these values, respectively. The results of the exponential random graph models support this framework. Specifically, hyperlinks are more likely to be created among neighborhood homeowner forums when the neighborhoods are located in the same administrative district, built by the same developers, and managed by the same property management companies. Unfavorable contexts that are prone to violent confrontation hamper the creation of cross-forum hyperlinks, but media visibility increases the odds of other forums hyperlinking to homeowner forums. In addition, high levels of online engagement are positively correlated with hyperlink formation. These findings suggest that although online platforms, such as homeowner forums, play a contributory role in collective action, they have limited power in fostering cross-neighborhood coalitions in urban China.     

Forging and Sustaining Labor–Community Coalitions: The Workfare Justice Movement in Three Cities

This article examines the factors shaping the formation and longevity of labor–community coalitions through comparative case studies of campaigns for workfare justice in Los Angeles, Milwaukee, and New York. Interviews with organizational staff and leaders reveal that their decisions to form and sustain these coalitions were shaped by their collective identities, especially their commitment to social movement unionism, and their context, particularly the sectoral distribution of workfare workers. We also highlight the role of two factors previously overlooked by labor scholars: (1) ecological processes of niche-formation, which determined if and how inter-organizational competition was overcome, and (2) authorities’ social-control strategies, which shaped coalition endurance.

Role analysis using the ego-ERGM: A look at environmental interest group coalitions

Interest groups coordinate to achieve political goals. However, these groups are heterogeneous, and the division of labor within these coalitions varies. We explore the presence of distinct roles in coalitions of environmental interest groups, and analyse which factors predict if an organization takes on a particular role. To model these latent dynamics, we introduce the ego-ERGM. We find that a group's budget, member size, staff size, and degree centrality are influential in distinguishing between three role assignments. These results provide insight into the roles adopted in carrying out coalition tasks. This approach shows promise for understanding a host of networks.     

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.     

DEBT BAILOUTS AND CONSTITUTIONS

A demand‐based theory of subnational debt bailouts is presented. It is shown that demand for bailouts among politicians with regional constituencies is affected by revenue sharing arrangements as a bailout implies a shift of taxation toward the federal tier. Automatic revenue sharing may lead to the formation of pro‐bailout coalitions formed by indebted states and states that are net recipients of the revenue sharing arrangement. The model shows that the state debt bailouts approved by the Brazilian Senate prior to the enactment of the Fiscal Responsibility Act were consistent with politicians who maximize the proceeds accruing to their constituencies. (JEL H70, D70)     

Minimum winning versus oversized coalitions in public finance: the role of uncertainty

This paper extends Persson et al.’s (J Polit Econ 108:1121–1161, 2000) simple legislature in the context of public finance with certainty to uncertainty. In our uncertain world, oversized coalitions (OSCs) as well as minimum winning coalitions (MWCs) may arise in equilibrium, and the agenda setter’s proposed policy may fail to receive a majority support. This is in marked contrast to the certain world, in which only MWCs can arise in equilibrium and the agenda setter’s proposal never fails to pass. When OSCs arise, we show that both public good provision and redistribution are likely to achieve their first-best solution, even if the legislature is simple.     

Spoilers,blocking coalitions,and the core

This paper surveys non-cooperative implementations of the core which tell an intuitive story of coalition formation. Under the core solution concept, if a blocking coalition exists those agents abandon the current allocation without regard for the consequences to players outside the blocking coalition. Yet in certain circumstances, these players have an incentive to prevent formation of any blocking coalition; a game analyzed in Lagunoff (Games Econ Behav 7:54–61, 1994) is vulnerable to such circumstances. To obtain all core allocations and only core allocations, a mechanism must either restrict the actions of non-members of a proposed coalition, or ensure that non-members are unharmed by the departure of the coalition. These requirements illustrate the core’s nonchalance toward agents not in blocking coalitions. The author gives special thanks to Beth Allen and Andy McLennan for their direction, and gratefully acknowledges valuable discussions with Roger Lagunoff, Hugo Sonnenschein, John Ledyard, Myrna Wooders, Nuray Akin, as well as comments from participants at the 2004 Spring Midwest Economic Theory and the Society for Economic Design conferences and from anonymous referees. All errors remain my own. Partial funding came from National Science Foundation grants DMI-0070257 and DMI-0217974.