社会福利函数独裁的特征

The Equivalent Conditions of Dictatorship for Social Welfare Functions

在这篇短文中,给出了关于社会福利函数F的半严格正向响应的概念,并且证明了如果备选对象至少有三个,则弱帕累托性质与半严格正向响应性质是独裁的充分必要条件.作为应用,我们给出了社会选择函数防止策略性操纵的一个等价描述,并对社会福利函数引进了防止局部策略性操纵的概念,得到了一个类似于Gibbard—Satterthwaite定理的结论.

We introduce the semi-strict monotonicity for social welfare functions. Then we prove that for any social welfare function F, whose range contains more than two alternatives and whose domain consists of all preference profiles, the semi-strict monotonicity and weak Pareto property are the sufficient and necessary conditions of dictatorship. As a application of our result, we generalized the Gibbard-Satterthwaite＇s Theorem to social welfare functions and given a equivalent condition of strategy-proofness for social choice.