A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one

I consider whether the agentsʼ reluctance to make a large lie is helpful for the rule designer to construct a nonmanipulable rule. For this purpose, I study an axiom, called AM-proofness, saying that manipulation cannot occur through preferences adjacent to the sincere one. Through examples, I give rationales for AM-proofness. My main result is a sufficient condition on a domain for the equivalence of AM-proofness and strategy-proofness. I show that the sufficient condition is satisfied by the universal domain and the domain of single-peaked preferences. Over such domains, all results about strategy-proofness can be restated with AM-proofness.