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Manipulability Comparisons of Positional Voting Rules for Large Three-Candidates Elections

Given any positional voting rule (PVR), a characterization of unstable voting situations is provided for three-candidate elections with large electorates. Our contribution to this literature concerns three aspects: (i) a comparison of PVRs via set inclusion of their corresponding sets of unstable voting situations; (ii) a full classification of PVRs according to their vulnerability to coalitional manipulation; and (iii) the determination of the maximal minimum size of a manipulating coalition. The attractiveness of the results obtained is that our conclusions are valid for the whole class of PVRs. It turns out that, under the Impartial Anonymous Culture (IAC), the PVR that minimizes the frequency of unstable voting situations is the plurality rule when the size of the manipulating coalition is unrestricted and the Borda rule for small manipulating coalitions.