Party policy and campaign costs in a multi-constituency model of electoral competition

In this essay, a multi-constituency model of electoral competition was developed under the assumption that party candidates possessed no effective autonomy. Such a model describes the polar extreme opposite that of the more common single constituency framework, in which candidates have complete autonomy. The existence of a Nash equilibrium to the multi-constituency election game was established under the assumption that parties maximize the expected number of winning seats or behaved as pure independents. Under any other reasonable election goal (e.g., maximize probability of winning a majority of constituencies), this existence breaks down. The nature of any equilibrium was investigated in some detail and the influence of campaign costs - both statutory and non-statutory - on party behaviour analysed. This was found to be qualitatively important. In particular, differing economic resources between parties is sufficient to prevent convergence in policy space. Multi-constituency models raise a whole set of new questions for the spatial theorist. It is clear that the now highly sophisticated single constituency model is insufficient for analysing party behaviour in more general political systems with no proportional representation. This is particularly evident in view of the negative result of section 4. This result also questions the appropriateness of the Nash solution as an equilibrium concept for election games. The generally fragile nature of this solution is well-known: in the present context, though, there is another reservation. Elections take place over a finite time period and observed policies, at least in emphasis, are altered during the campaign. Since the polling day(s) are constitutionally predetermined, there seems no reason why the election per se should occur when the parties offer equilibrium policies. And, since voter distributions change over time, we cannot a priori expect parties to offer essentially identical (spatial) policies at each election. Perhaps, then, we should be looking for optimal policy paths over the electoral period and across elections.