A BORDA MEASURE FOR SOCIAL CHOICE FUNCTIONS

The question addressed in this paper is the order of magnitude of the difference between the Borda rule and any given social choice function . A social choice function is a mapping that associates a subset of al ternatives to any profile of individual preferences. The Borda rule co nsists in asking voters to order all alternatives, knowing that the la st one in their ranking will receive a score of zero, the second lowes t a score of 1, the third a score of 2 and so on. These scores are the n weighted by the number of voters that support them to give the Borda score of each alternative. The rule then selects the alternatives wit h the highest Borda score. In this paper, a simple measure of the diff erence between the Borda rule and any given social choice function is proposed. It is given by the ratio of the best Borda score achieved by the social choice function under scrutiny over the Borda score of a B orda winner. More precisely, it is the minimum of this ratio over all possible profiles of preferences that is used. This ''Borda measure'' or at least bounds for this measure is also computed for well known so cial choice functions. (C) 1997 Elsevier Science B.V.