Bounded response of aggregated preferences

We propose a new axiom called bounded response, which says that the smallest change in an agent's preference leads to the smallest or no change in the aggregated preference in the society. This axiom can be interpreted as continuity or insensitivity of aggregated preferences with respect to the reported preferences. We show that bounded response together with a weak axiom imply dictatorship whenever there are four or more alternatives. This result shows that the continuity or the insensitivity of aggregated preferences, formulated as bounded response, with respect to the reported preferences is achieved only by dictatorship. Our result also offers a new perspective on Arrow's theorem: neither independence property nor informational efficiency in independence of irrelevant alternatives is necessary for the impossibility. Our result has an interesting implication also for “individual” problem of formulating an aggregated preference based on several criteria. A new technique is employed in the proof.