A celebrated result of Black (1984a) demonstrates the existence of a simple majority winner when preferences are single-peaked. The social choice follows the preferences of the median voter’s most preferred outcome beats any alternative. However, this conclusion does not extend to elections in which candidates diﬀer in more than one dimension. This paper provides a multi-dimensional analog of the median voter result. We show that the mean voter’s most preferred outcome is unbeatable according to a 64%-majority rule.