Essays on Bargaining and Voting Power

Abstract

The thesis contains five papers on measurement, properties, and foundations of bargaining and voting power.

‘The Public Good Index with Threats in A Priori Unions’ introduces four new variants of the Public Good Index (PGI) for simple games that have an a priori coalition structure. The first variant, the Union Public Good Index, is a natural extension of the PGI. The other three variants, called Threat Public Good Indices, distribute power based on the players’ threat power, which is their power in case they leave their union.

‘Axiomatizations of Public Good Indices with A Priori Unions’ provides comparable axiomatic characterizations for the Union PGI and Threat PGIs that build on arbitrary threat games.

‘Monotonicity of Power in Weighted Voting Games with Restricted Communication’ hence sets out to identify suitable monotonicity concepts weighted voting games which explicitly take into account the communication possibilities of players. Various monotonicy concepts suggest themselves for both available dimensions, the voting weights of players as well as their communication possibilities. These monotonicities can deal with either local comparisons of two players in the same game, or global comparisons of one and the same player in two different games. Then, the paper investigates the monotonicity properties of solution concepts such as the Myerson value, the restricted Banzhaf value, the position value, and the average tree solution.

The note ‘Veto Players and Non-Cooperative Foundation of Power in Coalitional Bargaining’ discusses the possibilities of non-cooperative support for power indices in the Baron-Ferejohn bargaining model. The discussion is based on the result that veto players either hold all power in this framework and then share it proportional to their recognition probabilities, or hold no power at all. Thus, non-cooperative support is restricted to power indices that either assign all or no power to veto players.

The fifth paper, ‘Coalitional Bargaining with Markovian Proposers’, provides an extension of the Baron-Ferejohn model to non-independent proposers. The non-independence of proposers significantly widens the scope of possible proposer dynamics, allowing for instance for likely continued offers, alternating proposers, and deterministic protocols such as clockwise rotating proposers. Although motivated by an example where two canonical proposer dynamics yield substantially different results for the power of veto players, reults show these qualtative differences are a mere singularity. Thus, the results show a great stability of support for the core and related single-valued concepts. At the same time, the possibilities of non-cooperative support for indices that do not assign all or no power to veto players are further limited to, at most, singular protocols.