A simpte solution for polyarchies which have not yet solved the problem of electing democratically a government and which have to cope with the problem of multipartism is proposed. The technique proceeds as follows: in a first round the electorate can make a choice between different candidates for the prime ministership. The candidate who obtains an absolute majority forms a government. If no candidate obtains an absolute majority, which is the most likely outcome, the two best placed candidates participate in a second round. However, each of these candidates now presents a complete government coalition to the electorate. The voters can choose between those two coalitions. The coalition with the majority of the vote becomes the government. The criticism against this proposal is being investigated. The new technique is illustrated on the basis of the political situation in Belgium.