Not obviously manipulable allotment rules

In the problem of allocating a single non-disposable commodity among agents whose preferences are single-peaked, we study a weakening of strategy-proofness called not obvious manipulability (NOM). If agents are cognitively limited, then NOM is sufficient to describe their strategic behavior. We characterize a large family of efficient and NOM rules, which we call ""simple"". The idea behind their definition has been dormant in the axiomatic literature for a long time. In economies with excess demand, simple rules fully satiate agents whose peak amount is no greater than equal division and assign, to each remaining agent, an amount between equal division and his peak. In economies with excess supply, simple rules are defined symmetrically. We also show that the single-plateaued domain is maximal for efficiency and NOM (together with other basic requirements). Therefore, even though replacing strategy-proofness with NOM greatly expands the family of admissible rules, the maximal domain of preferences involved remains basically unaltered.