We investigate when non-dictatorial aggregation is possible from an algorithmic perspective, where non-dictatorial aggregation means that the votes cast by the members of a society can be aggregated in such a way that the collective outcome is not simply the choices made by a single member of the society. We consider the setting in which the members of a society take a position on a fixed collection of issues, where for each issue several different alternatives are possible, but the combination of choices must belong to a given set X of allowable voting patterns. Such a set X is called a possibility domain if there is an aggregator that is non-dictatorial, operates separately on each issue, and returns values among those cast by the society on each issue. We design a polynomial-time algorithm that decides, given a set X of voting patterns, whether or not X is a possibility domain. Furthermore, if X is a possibility domain, then the algorithm constructs in polynomial time such a non-dictatorial aggregator for X. We also design a polynomial-time algorithm that decides whether X is a uniform possibility domain, that is, whether X admits an aggregator that is non-dictatorial even when restricted to any two positions for each issue. As in the case of possibility domains, the algorithm also constructs in polynomial time a uniform non-dictatorial aggregator, if one exists.
CITATION STYLE
Kirousis, L., Kolaitis, P. G., & Livieratos, J. (2018). On the computational complexity of non-dictatorial aggregation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11194 LNCS, pp. 350–365). Springer Verlag. https://doi.org/10.1007/978-3-030-02149-8_21
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