Frank Steffen

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.

Constrained Monotonicity and the Measurement of Power

In this paper we will discuss constraints on the number of (non-dummy) players and on the distribution of votes such that local monotonicity is satisfied for the Public Good Index. These results are compared to properties which are related to constraints on the redistribution of votes (such as implied by global monotonicity). The discussion shows that monotonicity is not a straightforward criterion of classification for power measures.

The Chairman’s Paradox Revisited

This paper 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 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. We also point to a new paradox of sophisticated voting.

On the Measurement of Success and Satisfaction

The main purpose of the present paper is to disentangle the mix-up of the notions of success and satisfaction which is prevailing in the voting power literature. We demonstrate that both notions are conceptually distinct, and discuss their relationship and measurement. We show that satisfaction contains success as one component, and that both coincide under the canonical set-up of a simultaneous decision-making mechanism as it is predominant in the voting power literature. However, we provide two examples of sequential decision-making mechanisms in order to illustrate the difference between success and satisfaction. In the context of the discussion of both notions we also address their relationship to different types of luck.

A Note on the Electoral Rules for the Welsh Assembly

A recent article in this journal highlights,using simulated data, potential paradoxes inherent in thesystem of election to the Welsh assembly. This paper examinesthe data for the assembly elections held in 1999 to illustratethe occurrence of yet another paradoxical outcome, theelection of the first ever First Minister due to a fall insupport for his own party.

Measuring Power and Satisfaction in Societies with Opinion Leaders: Properties of the Qualified Majority Case

A well known and established model in communication policy in sociology and marketing is that of opinion leadership. It is based on the idea of a two-step flow of communication. Opinion leaders are actors in a society who are able to affect the behavior of other members of the society called followers. Hence, opinion leaders might have a considerable impact on the behavior of markets and other social agglomerations being made up of individual actors choosing among a number of alternatives. For marketing purposes it appears to be interesting to investigate the effect of different opinion leader-follower structures in markets or any other collective decision-making situations in a society. We study a two-action model in which the members of a society are to choose one action, for instance, to buy or not to buy a certain joint product, or to vote yes or no on a specific proposal. Each of the actors has an inclination to choose one of the actions. By definition opinion leaders have some power over other actors, their followers, and they exercise this power by influencing the behavior of their followers, i.e. their choice of action. After all actors have chosen their actions, a decision-making mechanism determines the collective choice resulting out of the individual choices. The structure of the relations between the actors can be represented by a bipartite digraph. We analyze such digraphs investigating satisfaction and power distributions within societies with and without the opinion leaders. Moreover, we study common properties of the satisfaction and power measures and illustrate our findings and some marketing implications for a society with five members.