New characterizations of strategy-proofness under single-peakedness
提出了防策略性投票规则的新表示法（如“分级曲线”），统一了现有结果，并刻画了防策略性与序数性、参与性、一致性、比例性等结合时的特征，最后用新表示法计算了最大化事前社会福利的防策略性方法。
Abstract We provide novel representations of strategy-proof voting rules applicable when voters have uni-dimensional single-peaked preferences. In particular, we introduce a ‘grading curve’ representation which is particularly useful when introducing variable electorates. Our analysis recovers, links and unifies existing results in the literature, and provides new characterizations when strategy-proofness is combined with other desirable properties such as ordinality, participation, consistency, and proportionality. Finally, the new representations are used to compute the strategy-proof methods that maximize the ex-ante social welfare for the $$L_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -norm and a uniform prior. The resulting strategy-proof welfare maximizer is the linear median (or ‘uniform median’), that we also characterize as the unique proportional strategy-proof voting rule.