Electing a committee with constraints
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We consider the problem of electing a committee of k candidates, subject to some constraints as to what this committee is supposed to look like. In our framework, the pool of candidates is divided into tribes, and constraints of the form "at least p candidates must be elected from tribe X" and "there must be at least as many members of tribe X as of Y" are considered. In the case of a committee scoring rule this becomes a constrained optimisation problem and in the case of weakly separable rules we show the existence of a polynomial time solution in the case of tree-like constraints, and prove NP-hardness in the general case.
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