The various conditions for non-intransitivity of majority rule formulated over the past decade have been concerned with choices over arbitrary, usually finite, sets of discrete alternatives. In many economic and other social choice problems, however, the possible choices constitute a point set in some appropriately defined multi-dimensional commodity or policy space. It is shown that in problems of this kind, when voter preferences can be represented by quasi-concave, differentiable utility functions, the various equilibrium conditions for majority rule are incompatible with even a very modest degree of heterogeneity of tastes, and for most purposes are probably not significantly less restrictive than the extreme condition of complete unanimity of individual preferences.