A Research Note on the Size of Winning Coalitions

1971 ◽  
Vol 65 (3) ◽  
pp. 741-745 ◽  
Author(s):  
Robert Lyle Butterworth
Keyword(s):  
Coalition Formation ◽  
Theoretical Foundation ◽  
Winning Coalition ◽  
Research Note ◽  
Size Principle ◽  
Zero Sum Games ◽  
Upper Limit ◽  
Individual Player ◽  
Zero Sum ◽  
Rational Players

This paper is concerned with the problem of relating aggregate coalition payoffs to the winnings of an individual player, so that some theoretical foundation might be developed for dealing with problems of coalition formation. Professor William H. Riker was concerned with this problem in his Theory of Political Coalitions; in that book he developed a formulation holding that in several common political situations players would strive to form only minimum winning coalitions. Riker based that formulation on his derivation in game theory of “the size principle,” which held that in zero-sum games among rational players with perfect information, only minimum winning coalitions would occur. The first part of this research note shows that there is a difficulty in Riker's derivation of the “size principle,” presents counter-examples to that principle, and shows that it is unsound in general. The second part of this note develops the maximum number of positive gainers principle, which shows that in the kind of games being examined there is a maximum upper limit to the number of players who will positively gain; but this does not insure that the winning coalition will be minimal.

Hollow Victory: The Minimum Winning Coalition

1976 ◽  
Vol 70 (4) ◽  
pp. 1202-1214 ◽  
Author(s):  
Russell Hardin
Keyword(s):  
United States ◽  
House Of Representatives ◽  
General Class ◽  
Winning Coalition ◽  
The United States ◽  
Bargaining Game ◽  
Roll Call ◽  
Restricted Class ◽  
Size Principle ◽  
Zero Sum

The proof of Riker's size principle is inadequate for the general class of zero-sum bargaining games (whether symmetric or asymmetric), and the principle is valid only for a very restricted class of games—the supersymmetric games and their asymmetric counterparts. Butterworth's modification of the size principle (the maximum number of positive gainers principle) can be extended to cover games which are only approximately symmetric. Roll-call voting in the United States House of Representatives overwhelmingly violates the size principle; hence, the House does not generally play a supersymmetric zero-sum bargaining game. More generally, both Butterworth's and Riker's principles seem inapplicable to large bodies.

Decision Costs in Coalition Formation

1968 ◽  
Vol 62 (2) ◽  
pp. 556-563 ◽  
Author(s):  
Charles R. Adrian ◽  
Charles Press
Keyword(s):  
Decision Making ◽  
Coalition Formation ◽  
Winning Coalition ◽  
Competent Authority ◽  
The United States ◽  
United Nations Security Council ◽  
Coalition Building ◽  
Entire Group ◽  
Information Costs ◽  
Zero Sum

Choices made in coalition formation are costly to participants, complex, and difficult to measure with precision because observable coalitions are multi-person, non-zero-sum games. At least eight decision costs are included in the process. The purpose of this paper is to identify them and to examine their usefulness in explaining coalition formation. Decisions include: (1) information costs, (2) responsibility costs, (3) intergame costs, (4) costs of division of payoffs, (5) dissonance costs (6) inertia costs, (7) time costs, and (8) persuasion costs.Coalition building is an essential aspect of decision making within any political system. Whether one is studying the behavior of a municipal planning commission, a committee or sub-committee of a legislative body, the United Nations Security Council, or any other decision-making institution in which more than one person is involved in reaching a decision, the essential problem is often one of establishing a winning coalition within the entire group membership. A winning coalition is any portion of the group that can decide to do or not to do something that is on the agenda of the group and over which it has competent authority. The requirements of what constitutes a winning coalition are determined by the formal and informal rules of the game. Most commonly, one of the rules is that a winning coalition must consist of one-half the members of the group plus one and this assumption is made for purposes of this paper. The size of the coalition needed is important for individual and coalition strategies, but it is not important conceptually. That is, the problems involved in securing a winning coalition on the United States Supreme Court when only four votes are needed in order to agree to hear a case affects the strategy of the members of the court, but is of no theoretical importance to coalition formation.

On the Size of Winning Coalitions

1974 ◽  
Vol 68 (2) ◽  
pp. 505-518 ◽  
Author(s):  
Kenneth A. Shepsle
Keyword(s):  
Coalition Structure ◽  
Solution Theory ◽  
Size Principle ◽  
Zero Sum Games ◽  
Present Essay ◽  
Reasonable Solution ◽  
Person Game ◽  
Zero Sum ◽  
Special Case

A recent note by Robert Butterworth is critical of William Riker's size principle on several important grounds. There is, however, an important omission in his analysis which this present essay aims to correct. The author goes on to tie assertions about coalition structure in n-person zero-sum games to a solution theory for such games. In the appendix to this essay the general five-person game, of which Butterworth's game is a special case, is considered in some detail. The effect, with one reasonable solution theory, is a favorable appraisal of the size principle.

Ordinal Preference Games: An Analysis of Legislative Coalition Formation Without Transferable Utility

1983 ◽  
Vol 78 (3) ◽  
pp. 750-763 ◽  
Author(s):  
David H. Koehler
Keyword(s):  
Coalition Formation ◽  
Winning Coalition ◽  
Cardinal Utility ◽  
Size Principle ◽  
Political Issues ◽  
Ordinal Preferences ◽  
Ordinal Preference ◽  
Person Game ◽  
Voting Strategy

Two important findings from n-person game theory are that coalition formation is superadditive if and only if a game possesses an empty core, and Riker's size principle. Up to the present, both theorems have been proved and critiqued under the assumption of transferable cardinal utility.This analysis eliminates the cardinal utility assumption on the grounds that it is generally inconsistent with the conditions that characterize collective choice on political issues. Instead, a model of collective decision making is set forth in terms of ordinal preferences, and the two theorems are reconsidered. The superadditivity theorem survives intact, whereas the size principle is weakened. Circumstances are identified in which there is no incentive to reduce an oversized winning coalition; however, under no condition is there an incentive to increase the size of a winning coalition. A number of coalition-size hypotheses are tested using roll-call data from the U.S. Senate. The results raise new questions about the role of coalition formation in legislative voting strategy.

scholarly journals The 3P Challenge: A Serious Game for Reflecting on Partnership in Public-Private Concessions

2020 ◽  
pp. 1087724X2098158
Author(s):  
Camilo Benitez-Avila ◽  
Andreas Hartmann ◽  
Geert Dewulf
Keyword(s):  
Process Management ◽  
Project Managers ◽  
Serious Game ◽  
Public Private Partnerships ◽  
Mixed Group ◽  
Public Project ◽  
Zero Sum Games ◽  
Management Literature ◽  
Contractual Obligations ◽  
Zero Sum

Process management literature is skeptical about creating legitimacy and a sense of partnership when implementing concessional Public-Private Partnerships. Within such organizational arrangements, managerial interaction often resembles zero-sum games. To explore the possibility to (re)create a sense of partnership in concessional PPPs, we developed the “3P challenge” serious game. Two gaming sessions with a mixed group of practitioners and a team of public project managers showed that the game cycle recreates adversarial situations where players can enact contractual obligations with higher or lower levels of subjectivity. When reflecting on the gaming experience, practitioners point out that PPP contracts can be creatively enacted by managers who act as brokers of diverse interests. While becoming aware of each other stakes they can blend contractual dispositions or place brackets around some contractual clauses for reaching agreement. By doing so, they can (re)create a sense of partnership, clarity, and fairness of the PPP contract.

Coalition Formation and Selectorate Theory: An Experiment

2015 ◽  
Vol 5 (2) ◽  
pp. 261-275
Author(s):  
Andrew W. Bausch
Keyword(s):  
Public Goods ◽  
Laboratory Experiment ◽  
Coalition Formation ◽  
Winning Coalition ◽  
Private Goods ◽  
Target Individual ◽  
Selectorate Theory ◽  
Over Time

This paper uses a laboratory experiment to examine how different rules for re-selecting the leader of a group affects how that leader builds a winning coalition. Leaders play an inter-group game and then distribute winnings from that game within their group before standing for re-selection. The results of the experiment show that leaders of groups with large winning coalition systems rely heavily on distributing winnings through public goods, while leaders of groups with small winning coalition systems are more likely to target specific citizens with private goods. Furthermore, the experiment shows that supporters of small coalition leaders benefit from that support in future rounds by receiving more private goods than citizens that did not support the leader. Meanwhile, citizens that support a large coalition leader do not benefit from this support in future rounds. Therefore, small coalition leaders target individual citizens to maintain a coalition over time in a way not possible in a group with a large winning coalition. Finally, in the experiment, small coalition leaders increased their payoffs over time, suggesting that once power has been consolidated, small coalition leaders narrow their coalition.

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