Voting Weights and Formateur Advantages in the Formation of Coalition Governments

Abstract

We examine the relationship between parliamentary seats and cabinet posts in European governments between 1946 and 2001. Our speci¯cation improves on past studies in two respects. First, it derives and uses the voting weights of the underlying coalition formation games. This reduces the measurement error introduced when seat shares are used to proxy for voting weights. Second, the statistical model allows us to nest the predictions of di®er-ent formal theories of the distribution of posts. We¯nd that for non-formateur parties in the government, there is a linear relationship between their share of the voting weight in parliament and their share of cabinet posts. Additionally, the formateur party receives a substantial \bonus" relative to its voting weight. The latter¯nding is more consistent with proposal-based bargaining models of coalition formation, and less so with demand-bargaining models.

Proportional Payoffs in Legislative Bargaining with Weighted Voting: A Characterization

“…is still the case that a type [5] player ends up in the coalition with probability 3 5 , whereas a type [1] player only ends up in the coalition with probability …”

“…In particular, the ratios v [3] /v [1] and v [2] /v [1] are 5 and 4 respectively instead of 3 and 2. Intuitively, there is an excess demand for the mediumsize players.…”

“…and a small player is recognized with probability . Hence, the large players are getting a disproportionately high payoff since v [5] > 5v [1] .…”

“…Since each medium-size party can form a coalition with either the large party or the two smaller parties, one would expect v [3] = v [2] + v [1] . However, there is no particular reason to expect [1] . A player with 2 votes need not command a price equal to that of two players with 1 vote each, since no two players with 1 vote are available to replace the player with 2 votes.…”

“…There are two types of MWCs: the large party together with one of the medium-size parties, and the three smaller parties together. Let v [3] , v [2] and v [1] denote the expected equilibrium payoffs for a player with 3, 2 and 1 votes respectively. Since each medium-size party can form a coalition with either the large party or the two smaller parties, one would expect v [3] = v [2] + v [1] .…”