Cabinet Formation and Portfolio Distribution in European Multiparty Systems

Government formation in multiparty systems is of self-evident substantive importance, and the subject of an enormous theoretical literature. Empirical evaluations of models of government formation tend to separate government formation per se from the distribution of key government pay-offs, such as cabinet portfolios, between members of the resulting government. Models of government formation are necessarily specified ex ante, absent any knowledge of the government that forms. Models of the distribution of cabinet portfolios are typically, though not necessarily, specified ex post, taking into account knowledge of the identity of some government ‘formateur’ or even of the composition of the eventual cabinet. This disjunction lies at the heart of a notorious contradiction between predictions of the distribution of cabinet portfolios made by canonical models of legislative bargaining and the robust empirical regularity of proportional portfolio allocations – Gamson’s Law. This article resolves this contradiction by specifying and estimating a joint model of cabinet formation and portfolio distribution that, for example, predicts ex ante which parties will receive zero portfolios rather than taking this as given ex post. It concludes that canonical models of legislative bargaining do increase the ability to predict government membership, but that portfolio distribution between government members conforms robustly to a proportionality norm because portfolio distribution follows the much more difficult process of policy bargaining in the typical government formation process.Peer Reviewe

Cabinet formation and portfolio distribution in European multiparty systems

Government formation in multiparty systems is of self-evident substantive importance, and the subject of an enormous theoretical literature. Empirical evaluations of models of government formation tend to separate government formation per se from the distribution of key government pay-offs, such as cabinet portfolios, between members of the resulting government. Models of government formation are necessarily specified ex ante, absent any knowledge of the government that forms. Models of the distribution of cabinet portfolios are typically, though not necessarily, specified ex post, taking into account knowledge of the identity of some government ‘formateur’ or even of the composition of the eventual cabinet. This disjunction lies at the heart of a notorious contradiction between predictions of the distribution of cabinet portfolios made by canonical models of legislative bargaining and the robust empirical regularity of proportional portfolio allocations – Gamson’s Law. This article resolves this contradiction by specifying and estimating a joint model of cabinet formation and portfolio distribution that, for example, predicts ex ante which parties will receive zero portfolios rather than taking this as given ex post. It concludes that canonical models of legislative bargaining do increase the ability to predict government membership, but that portfolio distribution between government members conforms robustly to a proportionality norm because portfolio distribution follows the much more difficult process of policy bargaining in the typical government formation process

On weights and quotas for weighted majority voting games

In this paper, we analyze the frequency distributions of weights and quotas in weighted majority voting games (WMVG) up to eight players. We also show different procedures that allow us to obtain some minimum or minimum sum representations of WMVG, for any desired number of players, starting from a minimum or minimum sum representation. We also provide closed formulas for the number of WMVG with n players having a minimum representation with quota up to three, and some subclasses of this family of games. Finally, we complement these results with some upper bounds related to weights and quotas.Peer ReviewedPostprint (published version

Forms of representation for simple games: sizes, conversions and equivalences

Simple games are cooperative games in which the benefit that a coalition may have is always binary, i.e., a coalition may either win or loose. This paper surveys different forms of representation of simple games, and those for some of their subfamilies like regular games and weighted games. We analyze the forms of representations that have been proposed in the literature based on different data structures for sets of sets. We provide bounds on the computational resources needed to transform a game from one form of representation to another one. This includes the study of the problem of enumerating the fundamental families of coalitions of a simple game. In particular we prove that several changes of representation that require exponential time can be solved with polynomial-delay and highlight some open problems.Peer ReviewedPostprint (author’s final draft