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The finantial support of the Junta de Castilla y León (Consejería de Educación y Cultura, Proyecto VA09/98) is gratefully acknowledged. The authors are indebted to Maurice Salles and two anonymous referees for their valuable comments and helpful suggestions.Abstract. This paper studies by means of reciprocal fuzzy binary relations the aggregation of preferences when individuals show their preferences gradually. We have characterized neutral aggregation rules through functions from powers of the unit interval in the unit interval. Furthermore, we have determined the neutral aggregation rules that are decomposable and anonymous. In this class of rules, the collective intensity of preference is the arithmetic mean of the values assigned by a function to the individual intensities of preference. We have also considered the neutral aggregation rules based on quasiarithmetic means. We have established that this class of rules generalizes the simple majority, when individuals have ordinary preferences and collective preferences are reciprocal.

In this paper a class of voting procedures, located between simple and unanimous majorities, is introduced and characterized. Given two alternatives, the winning alternative is the one with a number of votes exceeding that obtained by the other in a previously fixed quantity. Moreover, a subclass of these voting procedures has been considered, by demanding additionally a number of votes greater than a previously fixed threshold. The main results of this paper are characterizations of these voting procedures through aggregation functions of fuzzy preferences associated with quasiarithmetic means and OWA operators.

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