One-dimensional mechanism design
研究一维集体决策问题，证明存在一种规范性的峰值规则，能同时满足效率、防策略性、公平性和连续性，涵盖中位数投票定理和均匀配给规则等特例。
We prove a general possibility result for collective decision problems where individual allocations are one-dimensional, preferences are single-peaked (strictly convex), and feasible allocation profiles cover a closed convex set. Special cases include the celebrated median voter theorem (Black 1948, Dummett and Farquharson 1961) and the division of a nondisposable commodity by the uniform rationing rule (Sprumont 1991). We construct a canonical peak-only rule that equalizes, in the leximin sense, individual gains from an arbitrary benchmark allocation: it is efficient, group-strategyproof, fair, and (for most problems) continuous. These properties leave room for many other rules, except for symmetric nondisposable division problems.