The impact of fuzziness in social choice paradoxes

Abstract

Since Arrow's main theorem showed the impossibility of a rational procedure in group decision making, many variations in restrictions and objectives have been introduced in order to find out the limits of such a negative result. But so far all those results are often presented as a proof of the great expected difficulties we always shall find pursuing a joint group decision from different individual opinions, if we pursue rational and ethical procedures. In this paper we shall review some of the alternative approaches fuzzy sets theory allows, showing among other things that the main assumption of Arrow's model, not being made explicit in his famous theorem, was its underlying binary logic (a crisp definition is implied in preferences, consistency, liberty, equality, consensus and every concept or piece of information). Moreover, we shall also point out that focusing the problem on the choice issue can be also misleading, at least when dealing with human behaviour.