Two strict preference aggregation mechanisms are suggested. One determines the collective preference from the most preferred to the least preferred alternative using as inputs the individuals' most preferred alternatives once the alternatives already assigned a position in the collective preference have been removed. The other mechanism does the same the other way around, constructing the preference starting from the least preferred alternative and using the least preferred remaining alternatives as inputs. It is shown that if both procedures are assumed to generate the same collective preference then the resulting aggregation rule must be dictatorial or constant. Weaker versions of these procedures also yield a dictatorial aggregation rule when combined with mild versions of unanimity or surjectivity.