Borda rule, Copeland method and strategic manipulation.
The authors compare the susceptibility to manipulation of the Borda method (chosen as the canonical positional method) and the Copeland method (as representative of methods satisfying the Condorcet principle). The authors restrict themselves to elections with three alternatives where there are no ties in the rankings of individual voters. The alternatives give an (alphabetical) ordering that is used to break aggregate ties. The authors give characterizations of the voting situations in which the two methods are manipulable by a single voter, and thus compute vulnerability measures for each method. The conclusion is that, while vulnerability for both systems unsurprisingly decreases as the number of voters increases, the Borda method is always and substantially more vulnerable than the Copleand method. In the case of manipulation by coalitions of voters, the authors give numerical results for small systems to show that Borda is again more vulnerable than Copeland, but the computational complexity prevents them from giving an analytic formula to describe the Borda vulnerability measure in general. The authors also give an example to show that there are situations in which the Copeland method is manipulable but the Borda result is not, thus showing that there is not a simple inclusion between the two sets.
scientific article; zbMATH DE number 1925593