Extension of Some Voting Systems to the Field of Gradual Preferences

In the classical theory of social choice, there exist many voting procedures for determining a collective preference on a set of alternatives. The simplest situation happens when a group of individuals has to choose between two alternatives. In this context, some voting procedures such as simple and absolute special majorities are frequently used. However, these voting procedures do not take into account the intensity with which individuals prefer one alternative to the other. In order to consider this situation, one possibility is to allow individuals showing their preferences through values located between 0 and 1. In this case, the collective preference can be obtained by means of an aggregation operator. One of the most important matter in this context is how to choose such aggregation operator. When we consider the class of OWA operators, it is necessary to determine the associated weights. In this contribution we survey several methods for obtaining the OWA operator weights. We pay special attention to the way the weights are chosen, regarding the concrete voting system we want to obtain when individuals do not grade their preferences between the alternatives.