Essays in Power, Freedom, and Success : Concepts, Measurement, and Applications

This dissertation comprises a collection of self-contained game theoretical essays on different and detailed facets of power, freedom, and success. Chapter 1 is a brief introduction to the basic meaning of these concepts and their importance in welfare economics. The chapter includes a brief tour of the essays and how they conceptually and methodologically tie together. Chapter 2, ‘Preferences and the Measurement of Power’, which was written in collaboration with Manfred J. Holler and forthcoming in Journal of Theoretical Politics, 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. This essay argues 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 effect outcomes’. It is claimed that power resides in, and only in, a game form and not in a game itself. Chapter 3, ‘The Measurement of Freedom’, which has been submitted to the American Political Science Review (APSR), is about the measurement specific freedoms – the freedom of an agent to undertake some particular action. In a recent paper in the APSR, 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 right or freedom and that describes the expectation that a person may have about being in a position to exercise (‘being free to perform’) that freedom or legal right. An examination of the literature shows that such a measure has never been properly defined. Based on the framework of a game form, this essay develops a very simple and natural measure of specific freedom that turns out to be the conditional variant of ‘success’, a measure that we know from the literature on voting power. Some properties and characteristics of the measure are discussed. Chapter 4, ‘The Success of a Chairman’, 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 that do not allow for players to be indifferent 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. A new paradox of sophisticated voting is also detected and discussed. Chapter 5, ‘Voting Rules in Insolvency Law: A Simple-Game Theoretic Approach’, which was written in collaboration with Frank Steffen and published in the International Review of Law and Economics concerns an analysis of the voting rules in modern insolvency law. A chief characteristic of this 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 analysed in any rigorous manner. This paper provides an approach based upon the theory of simple games to analyse 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. Particular attention is given to the role of classification and the effect of coalition formation.

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