Some impossibility results with domain restrictions
Abstract The structure of power is examined in the Social Choice Function (SCF) framework when the domain of the SCF admits sets containing at least k elements, where k is any positive integer less than the number of alternatives in the universal set. In particular, when k > 2, pairs of alternatives are not included in the domain so that the existence of the “base relation” is not guaranteed and hence the usual proof of Arrow type impossibility results are no longer available. However, it is shown that most of the major Arrow type impossibility results reappear even when the domain is restricted in the above fashion.