A new democracy paradigm is emerging through participatory budgeting exercises, which can be defined as a public space in which the government and the society agree on how to adapt the priorities of the citizenship to the public policy agenda. Although these priorities have been identified and they are likely to be reflected in a ranking of public policy actions, there is still a challenge of solving a portfolio problem of public projects that should implement the agreed agenda. This work proposes two procedures for optimizing the portfolio of public actions with the information stemming from the citizen participatory exercise. The selection of the method depends on the information about preferences collected from the participatory group. When the information is sufficient, the method behaves as an instrument of legitimate democracy. The proposal performs very well in solving two real-size examples. 1. Introduction Even in the best scenarios, designing public policies is far from being an exact science, with quantitative determinations beyond all subjectivity. Without denying the objective content of the social interest, it is certain that the difficulty in apprehending it opens space to methods that seek to model the preferences of concrete individuals, able to express their preferences in a more or less consistent way. Up to now, democracy in the distribution of public resources has been fundamentally expressed in(i)the action of groups empowered by the society to make budget decisions on its behalf (GESBD) (parliaments, communes, governing boards of public organizations), formed by members of the political class legitimized by the popular vote, but that respond to their personal and their party’s interests instead of to the will of the electorate,(ii)the action of GESBDs formed by officials and experts appointed by the executive power that rather than interests of the electorate, reflected only in a very indirect way, reflect policies already designed by the executive. (iii)the attempts of participatory budgeting carried out at local level where the population’s priorities are directly heard by constituted authorities and are later reflected in the distribution of resources once the compatibility with the opinions of the political class has been achieved. Since its emergence in Porto Alegre, Brazil, participatory budgeting has spread to hundreds of Latin American cities and dozens of cities in other continents. “Participatory budgeting” can be defined as a public space in which the government and the society agree how to adapt the priorities of the
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