An impossibility under bounded response of social choice functions

•We consider a new axiom “bounded response” of social choice functions.•We show that bounded response is weaker than strategy-proofness.•Bounded response and efficiency imply dictatorship on the universal domain.

We introduce a new axiom called bounded response, which states that for each “smallest” change of a preference profile, the change in the social choice must be “smallest,” if any, for the agent who induces the change in the preference profile. We show that bounded response is weaker than strategy-proofness, and that bounded response and efficiency imply dictatorship. This impossibility has a far-reaching negative implication: on the universal domain of preferences, it is difficult to identify a non-manipulability condition that leads to a possibility result.