Received 30 June 2015, Revised 15 August 2016, Accepted 17 August 2016, Available online 24 August 2016Models of single district plurality elections show that with three parties anything can happen – extreme policies can win regardless of voter preferences. I show that when single district elections are used to fill a legislature, we get back to a world where the median voter matters. An extreme policy will generally only come about if it is preferred to a more moderate policy by the median voter in a majority of districts. The mere existence of a centrist party can lead to moderate outcomes even if the party itself wins few seats. I also show that, while some voters in a district will not vote for their nationally preferred party, in many ...