Justificaciones de la regla de Bordauna revisión crítica

Abstract

Under the Borda voting rule each voter assigns equidistant descending scores to candidates by order of merit. In this way, if there are n alternatives, the best of them obtains n-1 points, the second best n-2 points, and so on, up to the worst candidate, which is given 0 points. These individual values are added up in order to determine a collective outcome, the highest scored alternative(s) being the winner(s). Concerning the Borda count, which has provided a wide literature in Social Choice Theory, a question has arisen, even from Borda�s times: Why such range of scores (positive integer numbers) instead of other possible choices? This paper critically surveys the answers to the subject of arbitrariness of weights appearing in the Borda count. Firstly, the �philosophical� arguments by Borda (1770) himself and Laplace (1795), taking into account statistical hypotheses of equiprobability, or the apology by Morales (1797, 1805) considering the Borda count as the appropriate way to �calculate the opinion�; in second place, more recent approaches with axiomatic method such as those proposed by Goodman � Markowitz (1952) and more successfully by Young (1974, 1975), or the �partial justification� provided by Black (1976); then, metric treatments by Cook � Seiford (1982) (coming from Kendall (1962)) and Farkas � Nitzan (1979), or within the DEA context; finally, Saari�s defence with geometric techniques considering the Borda rule as the optimal method in collective decision making.