We propose a two-stage process called minority voting to allocate public projects in a polity. In the first period, a society decides by a simple majority decision whether to provide the public project. If the proposal in the first period is rejected, the process ends. Otherwise the process continues, but only the members of the minority keep agenda and voting rights for the second stage, in which the financing scheme is determined. In the second stage, the unanimity rule or the simple majority rule is applied. We provide a first round of relative welfare comparisons between minority voting and simple majority voting and outline our research program.