On the frontier between possibility and impossibility theorems in social choice

This paper attemts to make precise the frontier between possibility and impossibility theorems in social choice. It is shown that some criterion of rejection of some alternative is the critical factor. In the absence of such a condition, it is possible to construct a fairly wide class of “democratic” decision rules which satisfies a class of consistency conditions. Any one of these, together with the criterion of rejection, generates a power structure similar to the ones discovered by Arrow, Gibbard, and others when the decision rule is required to satisfy the weak Pareto principle and the independence condition.