Quasitransitive Social Choice Without the Pareto Principle

The underlying observation of this paper is that when the Pareto principle fails, the collection X of alternatives may be partitioned into a set X^* of unbeatable (against at least one member of X) elements and its complement X~X^* on which the Pareto axiom holds. It is then instructive to characterize the decisive, antidecisive and blocking coalitions for X~X^*against X~X^*, X~X^* against X^*, X^* against X~X^*, and X^* against X^*. Now X^* itself may contain elements which are unbeatable with respect to alternatives in X^*—this is to say that the Pareto axiom fails again. Thus X^* may be partitioned into 〖〖(X〗^*)〗^*=X^(2*)and X^*~X^(2*), locally on X^*, and then the same analysis that was applied in the case of the partition (X^*,X~X^*) can be employed again. This process is iterated until X^(n*) = Φ or X^(n*)=X^((n+1)*), for some n.