The Basic Arithmetic of Legislative Decisions

Despite the huge number of possible seat distributions following a general election in a multiparty parliamentary democracy, there are far fewer classes of seat distribution sharing important strategic features. We define an exclusive and exhaustive partition of the universe of theoretically-possible n-party systems into five basic classes, the understanding of which facilitates more fruitful modeling of legislative politics, including government formation. A common class of legislative party system has a “strongly-dominant” party in the privileged position of being able to play off the other parties against each other. Another is a “top-three” party system in which the three largest parties are perfect substitutes for each other in the set of winning coalitions, but no other party is ever pivotal. Having defined a partition of legislative party systems and elaborated logical implications of this partition, we classify a large set of postwar European legislatures. We show empirically that many of these are close to critical boundary conditions, so that stochastic processes involved in any legislative election could easily flip the resulting legislature from one type to another. This is of more than hypothetical interest, since we also show that important political outcomes differ systematically between the classes of party system – outcomes that include duration of government formation negotiations, type of coalition cabinet that forms, and stability of the resulting government. * Thanks to Steven Brams, Macartan Humphreys, Ben Lauderdale, and Alastair Smith for conversations and comments on versions of this paper. The arithmetic of legislative decisions / 1