On minimum sum representations for weighted voting games

A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the "yea" voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum, where the weights and the quota are restricted to be integers. Freixas and Molinero have classified all weighted voting games without a unique minimum sum representation for up to 8 voters. Here we exhaustively classify all weighted voting games consisting of 9 voters which do not admit a unique minimum sum integer weight representation.Comment: 7 pages, 6 tables; enumerations correcte

Bounds for the diameter of the weight polytope

A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out that the diameter can be upper bounded in terms of the maximum weight and the quota or threshold. We apply those results to approximation results between power distributions, given by power indices, and weights.Comment: 16 pages; typos corrected; arXiv admin note: text overlap with arXiv:1802.0049

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

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