Evaluating the Degree of Manipulability of Certain Aggregation Procedures under Multiple Choices

The problem of manipulation in voting is studied in the case of multi-valued choice. Well-known and new schemes of preferences extension enabling one to compare all possible social choices under an arbitrary number of alternatives are presented. The known indices of degree and efficiency of manipulation are described, and new indices are introduced. These preference extension schemes and indices are used for computer-aided evaluation of the degree and efficiency of manipulation of the known voting procedures allowing multi-valued choices. The results obtained are presented for five voting rules.