Assessing Borda’s Rule and Its Modifications

Abstract

The BC is a positional voting procedure fairly often applied in non-political choice settings. It has a usual mixture of good and bad theoretical properties. It is monotonic and consistent and excludes the election of an eventual Condorcet loser. It, however, does not necessarily choose the Condorcet winner when one exists. Its strategic properties have also been found unattractive. Some modifications to it have therefore been proposed, notably Nanson’s method. We also compare the BC with two of its recent modifications, the MBC and the QBS. It turns out that, although similar in spirit to BC, MBC and QBS do not share one of the former’s main justifications: the exclusion of an eventual Condorcet loser. It is also shown that QBS tends to lead to more majoritarian outcomes than BC. We also touch upon the matrix vote which enables the voter to express his/her views on both candidates and positions simultaneously.