We consider settings where a collection of agents express preferences over a set of candidates with a combinatorial structure via the use of CP-nets, and we need to exploit the information contained in the CP-nets to choose one of the candidates. Moreover, there is a set of constraints which defines the unfeasible candidates, which cannot be the result of the preference aggregation. We propose a method to achieve this which is based on voting, and considers one variable at a time in a sequence. This method has been studied in the literature to aggregate non-constrained CP-nets. Here we generalise it to work with constrained CP-nets, and we study its properties. The constraints are used to leave in the variable domains only the admissible values. This allows the voting steps to return only feasible values. We find conditions of coherence between the preference expressed in the CP nets and the constraints, in order to guarantee that the classical sequential aggregation method always returns a feasible candidate. Even when such conditions are not met, but the constraints defining the unfeasible candidates have a tree structure (or a structure with bounded tree-width), and the collection of CP-nets is O-legal (that is, the dependency graphs of the CP-nets are compatible), we show that our more general voting procedure can be used, and that it is polynomial in the number of features describing the candidates and in the number of voters.
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