Manfred J. Holler

FORMING COALITIONS AND MEASURING VOTING POWER

I N this paper I will present various concepts of coalition formation and power measures and discuss them with respect to the view ‘that situations where minor players possess greater potential for power are not anomalous, but occur rather frequently in real-world situations’.’ We shall see that the analysis of the various concepts of coalition formation will teach us much about the implications of the so-called power indices and the character of a priori voting power. A new index will be introduced which considers the coalition value of a public good and takes into consideration the distinction between power and luck. The values of this index will be calculated for the parties of the Finnish Parliament (Eduskunta) for the period 1948-79.

Power, luck and the right index

SummaryWe have pointed out the theoretical drawbacks of the traditional indices for measuring a priori voting power inasmuch as they are implied in considering the coalition value a private good. This criticism caused us to view the coalition outcome as a public good. From this aspect and additional considerations with respect to power, luck, and decisiveness, we obtained a “story” describing the characteristics of an adequate measure of a priori voting power. These characteristics were found to be fulfilled by an index presented by Holler (1978). Through the above analysis this index has received its theoretical justification. An independent view of this index was then provided by means of an axiomatic characterization. This characterization makes possible abstract comparison of the index with previously established “private good” indices.While we have restricted our attention to simple games, the index presented can be generalized to provide a “value” on games in characteristic function form. We leave this topic for future conideration.

Power, Voting, and Voting Power

1. Introduction.- An Introduction to the Analysis of Power, Voting, and Voting Power.- 2. The Idea of Power.- Power in Game Forms.- A Philosophical View of Power.- Power and Profit in Hierarchical Organizations.- Equivalent Concepts of Power in Voting Games.- Attribution and Social Power.- Power: An Amorphous Term - Diverse Conceptual Approaches.- 3. Formal Analysis of Representation and Voting Procedures.- Proportional Representation and Effective Number of Parties in Finland.- The Relationship Between Voting and Party Strength in an Electoral System.- Manipulation of the Agenda by Strategic Voting: Separable and Nonseparable Preferences.- Order-of-Voting Effects.- Strategic Voting in Multicandidate Elections under Uncertainty and under Risk.- Electoral Rules and Rational Voting: The Effects of Candidate Viability Perceptions on Voting Decisions.- 4. Concepts of Power Measurement.- The Problem of the Right Distribution of Voting Power.- An Axiomated Family of Power Indices for Simple n-Person Games.- Measuring Power in Voting Bodies: Linear Constraints, Spatial Analysis, and a Computer Program.- Modification of the Banzhaf-Coleman Index for Games with A Priori Unions.- Power and Satisfaction in an Ideologically Divided Voting Body.- Power in an Ideological Space.- Measuring Power.- 5. The Empirical Approach.- Party Power and Government Formation: A Case Study.- The Distribution of Power in Specific Decision-Making Bodies.- Political Geography and Political Power.- Regional Power Allocation: The Problem of British Devolution.- The Paradox of Redistribution: Some Theoretical and Empirical Results.

The Impossibility of a Preference-Based Power Index

This paper examines a recent debate in the literature on power indices in which classical measures such as the Banzhaf, Shapley-Shubik, and Public Good indices have been criticized on the grounds that they do not take into account player preferences. It has been argued that an index that is blind to preferences misses a vital component of power, namely strategic interaction. In this vein, there has been an attempt to develop so-called strategic power indices on the basis of non-cooperative game theory. We argue that the criticism is unfounded and that a preference-based power index is incompatible with the definition of power as a generic ability: ‘the ability to affect outcomes’. We claim that power resides in, and only in, a game form and not in a game itself.

Why Power Indices for Assessing European Union Decision-Making?

In this paper we argue that spatial voting games and power index models are not necessarily exclusive ways to analyse EU decision-making. We find that the two main criticisms pointed out by scholars of spatial voting games, namely that power indices do not take into account preferences or the role of the agenda-setter, are not fully valid as spatial voting games deal with complete whereas power indices deal with incomplete contracts. Ideas for combining the two so far very opposite views are then discussed.

Computing power indices: Multilinear extensions and new characterizations

Abstract Johnston [Johnston, R.J., 1978. On the measurement of power: some reactions to Laver. Environment and Planning A 10, 907–914], Deegan and Packel [Deegan, J., Packel, E.W., 1979. A new index of power for simple n -person games. International Journal of Game Theory 7, 113–123], and Holler [Holler, M.J., 1982. Forming coalitions and measuring voting power. Political Studies 30, 262–271] proposed three power indices for simple games: Johnston index, Deegan–Packel index, and the Public Good Index. In this paper, methods to compute these indices by means of the multilinear extension of the game are presented. Furthermore, a new characterization of the Public Good Index is given. Our methods are applied to two real-world examples taken from the political field.

Fighting pollution when decisions are strategic

In this paper we analyse anti-pollution policies in a 2-by-2 game played between a “polluter” and the “police” in which the payoffs can be manipulated by an exogenous third player called the “policy-maker.” We show that the efficiency of the policies may depend on whether the players of the 2-by-2 game choose Nash equilibrium strategies or prefer maximin.

Strict proportional power in voting bodies

It is a widely known fact among game theorists as well as political scientists that the distribution of voting weights in a voting body is generally a poor proxy for the distribution of voting power within the body. It has been proposed to equate the distribution of a priori voting power and actual seat distribution by randomizing the decision rule of the voting body over various majority rules. In this paper, some implications of this procedure will be discussed.

Freedom of Choice, Power, and the Responsibility of Decision Makers

Democracy, Freedom and Coercion comprehensively covers both private and public law, both applied and theoretical issues, and will therefore be of great interest to students studying law and economics.

Two Stories, One Power Index

This paper demonstrates that the mathematical properties of the member bargaining power measure (MBP) are identical with those of the public good index (PGI). However, the underlying theoretical concepts of the two measures are different. The MBP refers to bargaining over shares of the coalition value, and thus has a private good perspective, whereas the PGI considers power with respect to providing a public good as coalition value. The identity of the mathematical properties is used to study the properties of the two measures. For weighted voting games, both measures violate monotonicity with respect to voting weights, and the paradox of weighted voting applies.