Why small, centrist third parties motivate policy divergence by major parties

Plurality-based elections between two major parties or candidates sometimes feature small, centrist, third parties. We modify the standard two-party spatial model of policy-seeking parties to incorporate a centrist third party, and we show that the presence of such a party-even if it has no chance of winning-motivates the major parties to propose policies that are much more divergent than without the third party. We derive explicit formulas for party locations at a three-party equilibrium and provide necessary and sufficient conditions for existence of that equilibrium. We show that, over time, the major parties can be expected to shift their policies in the same direction relative to each other but in the opposite direction relative to the minor party. The predictions of this model are compared with estimates of party policy locations during appropriate periods in postwar Britain.