Fringe Candidates in Electoral Competition

I study a one-dimensional Hotelling-Downs model of electoral competition in which unelectable fringe candidates with extreme policy platforms are an integral part of the political process. When the preferences of voters change over time, and there are restrictions on political parties changing their platforms, the main parties will not respond to changes in voter preferences unless threatened by fringe candidates. It is rational for fringe candidates to run once and increase the victory chances of the party furthest from them, in order to move party platforms and the subsequent laws towards the fringe candidate's preferences in the long term