Minimal Determining Set and Its Unique Existence under Independent Decisiveness Condition ⅡA(S2)
-
摘要: 研究了当独立决定条件ⅡA(S1)弱化为ⅡA(S2)时,在非二元性选择环境下,选择函数的最小决定集及其唯一存在性.证明了在k-集可行性条件、无约束域条件、Pareto优化准则和独立决定条件ⅡA(S2)下,选择函数存在唯一的最小否定集和最小决定集.进而证明了在上述条件下,选择函数满足独立决定条件ⅡA(S2)的充分必要条件不是独裁者,而是寡头控制.Abstract: The minimal determining set of social choice function and its unique existence condition were investigated under non-binary choice and the condition that independent decisiveness condition ⅡA(S1) becomes independent decisiveness condition ⅡA(S2).It is proven that the unique minimal determining set and minimal veto set of the choice function exist under the conditions that the choice function satisfies the k-set feasible condition,the unrestricted domain,the Pareto optimality and the independent decisiveness condition ⅡA(S2),and the choice function satisfies the independent decisiveness condition ⅡA(S2) under the above-mentioned conditions if and only if it is oligarchic but not dictatorial.
-
Arrow K.Social choice and individual values(2nd ed)[M].New York:Wiley,1963:1-30.[2] BAIGENT N.Twitch weak dictators[J].J.Econ,1987,47(4):407-411.[3] SEN A K.Internal consistency of choice[J].Econometrica,1993,61(3):495-521.[4] VINCENZO D (O).Independent Decisiveness and the Arrow theorem[J].Social Choice and Welfare,1998,15(4):563-566.[5] 罗云峰,朱明富,岳超源,等.非二元性选择函数的Arrow不可能性定理[J].系统工程,1998,16(3):13-20.LUO Yunfeng,ZHU Mingfu,YUE Chaoyuan,et al.Choice function non-binariness revealed preference impossibility theorem[J].Systems Engineering,1998,16(3):13-20.[6] 郭耀煌,刘家诚,刘常青,等.格序决策[M].上海:上海科技出版社,2003:1-150.GUO Yaohuang,LIU jiacheng,LIU changqing,et al.Lattice ordered decision-making[M].Shanghai:Shanghai Scienceand Technology Press,2003:1-150.[7] 郭耀煌,刘家诚,周文坤.格序决策行为公理体系及其效用函数存在惟一性定理[J].西南交通大学,2001,36(3):221-224.GUO Yaohuang,LIU Jiacheng,ZHOU Wenkun.Axioms for lattice ordered decision-making behavior and relative utility theorem[J].Journal of Southwest Jiao Tong University,2001,36(3):221-224.[8] 郭耀煌,刘家诚,刘常青.最小决定集与Arrow不可能性定理[J].系统工程,2000,18(2):13-16.GUO Yaohuang,LIU Jiacheng,LIU Changqing.Minimal determining set and arrow impossibllity theorem[J].Systems Engineering,2000,18(2):13-16.[9] SAARI G.Connecting and resolving Sen's and Arrow's theorems[J].Social Choice and Welfare,1998,15(2):239-261.[10] SCHWARTZ T.A really general impossibility theorem[J].Quality and Quantity,1982,16(6):493-505.[11] BIRKHOFF G.Lattice theory(Volume XXV)[M].Providence,Rhode Island:American mathematical society Colloqnium Publications,1973:1-280.[12] PLOTT C R.Path independence,rationality and social choice[J].Econometrica,1973,41(6):1 075-1 091.[13] GRETHER D M,PLOTT C R.Nonbinary social choice an impossibility theorem[J].Review of Economic Studies,1982,49(2):143-149.
点击查看大图
计量
- 文章访问数: 1132
- HTML全文浏览量: 75
- PDF下载量: 277
- 被引次数: 0