ITS DISAGREEABLE IMPLICATIONS about social choices have convinced many people that Arrow's impossibility theorem rests on unacceptably strong conditions. Dissatisfaction has centered on (but is not limited to) the conditions that the social ordering should be a weak ordering (WO) and that it should be independent of irrelevant alternatives (IIA). A long line of research, culminating in the results of Mas-Colell and Sonnenschein [18] and Fishburn [7], has shown, however, that the impossibility theorem is robust against reasonable relaxations of WO. (More accurately, if WO is weakened, say by waiving completeness or transitivity of the social ordering, and the remaining conditions are correspondingly strengthened to keep the problem interesting, the impossibility remains.) It seems that this line