COMPOSITION-CONSISTENT TOURNAMENT SOLUTIONS AND SOCIAL CHOICE FUNCTIONS

This paper introduces a new axiom for choice in preference profiles an d tournaments, called composition-consistency. A social choice functio n is composition-consistent if it is non-sensitive to the cloning of o ne or several outcomes. The key feature of the composition consistency property is an operation concept called multiple composition product of profiles. The paper provides a brief overview of some social choice functions studied in the literature. Concerning the tournament soluti ons, it is proved that the Top Cycle, the Slater and the Copeland solu tions are not composition-consistent, whereas the Banks, Uncovered Set , TEQ, Minimal Covering Set are composition-consistent. Moreover, we d efine the composition-consistent hull of a solution phi as the smalles t composition-consistent solution containing phi. The composition-cons istent hulls of the Top cycle and Copeland solutions are specified, an d we give some hints about the location of the hull of the Slater set. Concerning social choice functions, it is shown that Kemeny, Borda an d Minimax social choice functions are not composition-consistent, wher eas the Paretian one is composition-consistent. Moreover, we prove tha t the latter is the composition-consistent hull of the Borda and Minim ax functions.