Coalition and Party Formation in a Legislative Voting Game

We examine a legislative voting game where decisions are being made over both ideological and distributive dimensions, and legislators' preferences are separable over the two dimensions. In equilibrium legislators prefer to make proposals for the two dimensions together, rather than offering sequential proposals on the two dimensions separately. The equilibria exhibit interaction between the ideological and distributive dimensions and in any equilibrium there is a positive probability that a proposal is made and approved which excludes the median legislator (as defined over the ideological dimension), in contrast with a game where no distributive decision is being made. Moreover, in any stationary equilibrium there is more than one ideological decision that has a positive probability of being proposed and approved. We show that legislators can gain from forming political parties, and consider examples where predictions can be made about the composition of parties. We discuss the impact of political parties on the outcome.