Minimal Determining Set and Its Unique Existence under Independent Decisiveness Condition ⅡA(S2)
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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.
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