We study a scenario where elections are held and two parties, a traditional downsian party and a party implementing Participatory Democracy, compete to win elections. We examine in detail the options of the party representing Participatory Democracy to win. The Participatory Democracy party will celebrate an assembly if taking-o¢ ce, where any citizen-candidate can represent his ideal position. This will make evaluate the party as a lottery. We consider different assembly equilibria varying the number of candidates. We include the valence characteristic concept and show the different strategies of both parties according to the valence advantage over the opponent.España. Ministerio de Ciencia e Innovación SECO2008-03674/ECONEspaña. Junta de...