Non-manipulable partitioning

Consider the following social choice problem. A group of individuals seek to classify the elements of X as belonging in one of two sets. The individuals may disagree as to how the elements of X should be classified, and so an aggregation rule is applied to determine a compromise outcome. We require that the social classification should not be imposed, nor should it be manipulable. We prove that the only aggregation rules satisfying these properties are dictatorships.