This article offers a spatial theory to explain how a centrist third party gains votes via the ideological depolarization of its two main competitors towards the centre ground. Using the cases of British elections in 2001, 2005 and 2010, during which the two main parties, Labour and the Conservatives, were ideologically similar, the article reveals how perceived similarities between these parties led voters to turn to alternative issues and criteria – which benefited the third party, the Liberal Democrats – to decide their vote. Major parties therefore trade a proximity benefit of chasing the median voter against a separation benefit whereby votes can be lost due to voter indifference. The expectations are supported by analyses of vote choices using two measures of indifference, although the incentives do not apply equally in all three elections. The article reveals that indifference is not just relevant to voter abstention, as applied in existing spatial theories, but is also relevant to the basis of the vote choice and to votes for third parties. The implications are important for spatial models of party competition.