We define a multidimensional analogue of a single-peaked preference and generalize the notion of a median voter scheme. Every onto strategy-proof social choice function on a single-peaked domain is a generalized median voter scheme. Since a single-peaked preference can be identified unequivocally with its bliss point, one can view a social choice function as an Arrowian social welfare function. We show that a social choice function is strategy-proof iff, viewed as a social welfare function, it satisfies a monotonicity property. Finally, we investigate strategic decision making in hierarchical committees. Journal of Economic Literature Classification Numbers: C72, D71. © 1993 by Academic Press, Inc.