Matthew Braham

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.

Power, freedom, and voting

Social Power and Social Causation: Towards a Formal Synthesis.- Power Indices Methodology: Decisiveness, Pivots, and Swings.- Further Reflections on the Expediency and Stability of Alliances.- Positional Power in Hierarchies.- A Public Help Index.- Shapley-Shubik vs. Strategic Power: Live from the UN Security Council.- Modified Power Indices for Indirect Voting.- Pivotal Voting Theory: The 1993 Clinton Health Care Reform Proposal in the U.S. Congress.- Coalition Formation Theories Revisited: An Empirical Investigation of Aumanns Hypothesis.- Coalition Formation, Agenda Selection, and Power.- Democratic Defences and (De-)Stabilisations.- The Instability of Power Sharing.- The Power to Propose versus the Power to Oppose.- Divergence in the Spatial Stochastic Model of Voting.- Closeness Counts in Social Choice.- Freedom, Coercion, and Ability.- Guarantees in Game Forms.- Individual Control in Decision-Making and Attitudes Towards Inequality: The Case of Italy.- The Principle of Fairness: A Game Theoretic Model.- Power, Productivity, and Profits.- Trust, Responsibility, Power, and Social Capital.- Exploiting The Prince.

Voting rules in insolvency law: a simple-game theoretic approach

Abstract A chief characteristic of modern insolvency law in Canada, Germany, the UK, and the US is the provision for ‘workouts’ or ‘schemes of arrangement’ by which insolvent companies can attempt to rehabilitate the business. If reorganization is chosen, the debtor has to devise a plan of action which will be voted upon by claimants. The voting rules, however, differ in each jurisdiction to a greater or lesser extent and as yet have not been analyzed in any rigorous manner. This paper provides an approach based upon the theory of simple games to analyze the rules in terms of the ease which each of these regimes can pass (or hinder) plans and how these rules distribute value among claimants. We pay particular attention to the role of classification and the effect of coalition formation.

Romani migrations and EU enlargement

This paper examines the root causes of recent attempts by central and eastern European (CEE) Roma to seek asylum in the European Union (EU) and considers their future migration potential and its implications for EU enlargement. While a westbound Roma migration is not favoured by current member states, instruments designed to discourage it will have but short‐term effect as after EU enlargement CEE Roma will have the right of free movement within the EU. Any attempt to prevent migration will then be illegal; accepting such a migration is however likely to prove unpopular. The article shows that two instruments that ought to resolve the problem, the ‘Copenhagen Criteria’ and the Framework Convention for the Protection of National Minorities, are unlikely to do so and goes on to conclude by suggesting that Roma communities have as much a part to play in seizing the window of opportunity for integration, as do majority societies and governments in providing it.

Power and Preferences Again

We would like to begin our reply to Stefan Napel and Mika Widgrén’s (hereinafter N&W) comment on our article ‘The Impossibility of a Preferencebased Power Index’ in this journal (17(1): 137–57) by immediately correcting two minor – but not insignificant – errors and misunderstandings. First, the intention behind our article was not to advocate in favour of classical power measures such as the Shapley–Shubik or Banzhaf indices but to demonstrate that a particular form of criticism levelled at them is erroneous. Pointing out that a thesis is immune to a particular criticism does not count as advocacy. Second, N&W say that we ‘have claimed that indices based on utilitymaximizing and strategizing agents are not only unneeded, but undesirable and conceptually meaningless’. This is wrong. Our argument runs in the other direction: because preference-based indices are conceptually meaningless, they are undesirable and, therefore, unnecessary. N&W’s reversal of our argument gives the impression that we were being dogmatic – quite the contrary. Our exclusion of i ’s preferences in a measure of i ’s power is not based on some willy-nilly predilection but on a conceptual and semantic analysis of the term ‘power’ – unless, of course, one dons the position of saying that anything other than formal deduction is dogma. Now to the major issues.

Social power and social causation: towards a formal synthesis

An impressive list of economists, political scientists, and philosophers starting with Thomas Hobbes and including Herbert Simon (1957), James March (1955), Robert Dahl (1957, 1968), Felix Oppenheim (1961, 1976, 1981), William Riker (1964), Virginia Held (1972), and Jack Nagel (1975) have claimed that there are key and compelling similarities between what is ordinarily considered to be an ascription of social power and that which is considered under the more general rubric of causality. Hence to say: ‘i has (had) power to x’, is to assert that i can (did) cause an outcome x. ‘i has (had) power over j’ , is to assert that i can (did) cause j to act in a specific way (in a manner that he would not otherwise do).

Causation and the Measurement of Power

This note examines the application of the concept of causation to the con-struction of power indices. It is argued that if the modeling of power relations should capture the causal factors of an outcome then a power index should be based only on the set of minimal winning coalitions. The argument refers to Mackie’s inus conditions.

MEASURING SPECIFIC FREEDOM

This paper is about the measurement of specific freedoms – the freedom of an agent to undertake some particular action. In a recent paper, Dowding and van Hees discuss the need for, and general form of, a “freedom function” that assigns a value between 0 and 1 to a freedom or right and that describes the expectation that a person may have about being in a position to exercise (“being free to perform”) that freedom or right. An examination of the literature shows that there is as yet no agreed framework for defining such a function. Based on the framework of a game form, I develop a very simple and natural measure of specific freedom as the “conditional probability of success.” It is also shown that in an important way “negative freedom is membership of powerful coalitions.”

Voids or Fragmentation: Moral Responsibility For Collective Outcomes

Institutional rules create difficulties for the allocation of moral responsibility. One problem is the existence of responsibility voids, i.e. situations in which an outcome results from individual interactions but for which no one is responsible. Another is that responsibility can be fragmented in the sense that responsibility-bearing individuals may be responsible for different features of the outcome. This study examines both problems together. We show that for a large class of situations the two problems are logically dependent. More precisely, non-dictatorial decision procedures can only ensure the absence of voids if they allow for the fragmentation of responsibility.