Public Choice 112: 167–184, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. 167 Borda count versus approval voting: A fuzzy approach JOSÉ LUIS GARCÍA-LAPRESTA & MIGUEL MARTÍNEZ-PANERO ∗ Departamento de Economía Aplicada, Universidad de Valladolid, Valladolid, Spain; e-mail: lapresta@cpd.uva.es Accepted 6 March 2001 Abstract. In this paper we consider a fuzzy variant of the Borda count taking into account agents’ intensities of preference. This fuzzy Borda count is obtained by means of score grada- tion and normalization processes from its original pattern. The advantages of the Borda count hold, and are even improved, providing an appropriate scheme in collective decision making. In addition, both classic and fuzzy Borda counts are related to approval voting, establishing a unified framework from distinct points of view. 1. Introduction Among the great variety of methods in collective decision making, in this paper we shall focus our attention on a variant of the Borda count, the vote-counting scheme introduced in 1770 by Jean Charles de Borda. 1 This en- gineer and navy officer denounced in a Memory read in the French Academy of Sciences that the usual collective decision procedures (such as plurality rule) only considered the most preferred alternative for each agent, ignoring the rest. Taking into account this partial information, the final output could not faithfully reflect the agents’ preferences. Borda showed examples with this fault, and then advocated the following method: each agent ranks all the alternatives, and gives integer marks to each of them: the highest score, which coincides with the number of alternatives, to the most preferred; one point less to the next alternative; and so on, in a descent manner, till the least preferred is reached, which is given only one point. This Borda count was chosen by the French Academy of Sciences to select its members and, from that time on, it has been both criticized and praised. Some advantages and drawbacks of the method can be shown according to procedural and epistemic arguments. ∗ This paper has been partially supported by the Consejer´ ıa de Educaci´ on y Cultura de la Junta de Castilla y Le´ on (project VA09/98). The authors want to acknowledge the valuable comments of an anonymous referee.