A comparative analysis of group decision methods

This paper examines some explicit social choice functions that are generalizations of the simple majority decision rule. Two different classes of such functions for choice from among two or more alternatives are summation procedures and completions of Condorcet's criterion (an alternative with a simple majority over each other alternative shall win). A condition of permuted dominance satisfies typical summation methods, and a reduction principle is consistent with the Condorcet criterion. The permuted dominance condition and the reduction principle are incompatible with one another. A summation method (Borda) and a Condorcet completion method (Copeland) were compared by computer simulation. With the number of voters varied from 3 to 21 and the number of alternatives varied from 3 to 9, about 90 percent of the 70,000 cases examined had a common winner for the two methods.