Straightforward Elections, Unanimity, and Phantom Voters
Straightforward Elections, Unanimity, and Phantom Voters
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直接选举、一致同意和幽灵选民
DOI：
10.2307/2296962
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
J. Jordan
中科院分区：
文献类型：
--
作者：
Kim C. Border;J. Jordan
不可操纵的直接启示社会选择函数的特点是社会的空间是一个欧几里德空间的替代品和所有的选民有可分离的星型偏好与全球最佳。如果一个不可操纵的选择函数满足一个弱的不友好尊重条件（相当于有一个不受限制的范围），那么它将只取决于选民的理想点。此外，这样的选择函数将分解为一维机制的乘积，因为所选点的每个坐标仅取决于选民理想点的相应坐标。每个坐标函数也将是不可操纵的，并且尊重连续性。这种单向度的机制是不妥协的，因为选民不能采取极端的立场来影响选择，使之对他们有利。给出了不妥协选择函数的两个刻画。一个是在连续性条件方面，另一个是在“幻影选民”方面，即那些被选择的点不是任何选民的理想点。有许多这样的机制不是独裁的。然而，如果选择函数需要可微性，这就迫使它要么是常数，要么是独裁的。在多维情况下，偏好的不可分离性导致独裁，即使偏好被限制为二次的。
Non-manipulable direct revelation social choice functions are characterized for societies where the space of alternatives is a euclidean space and all voters have separable star-shaped preferences with a global optimum. If a non-manipulable choice function satisfies a weak unanmity-respecting condition (which is equivalent to having an unrestricted range) then it will depend only on voters' ideal points. Further, such a choice function will decompose into a product of one-dimensional mechanisms in the sense that each coordinate of the chosen point depends only on the respective coordinate of the voters' ideal points. Each coordinate function will also be non-manipulable and respect unanimity. Such one-dimensional mechanisms are uncompromising in the sense that voters cannot take an extreme position to influence the choice to their advantage. Two characterizations of uncompromising choice functions are presented. One is in terms of a continuity condition, the other in terms of "phantom voters" i.e. those points which are chosen which are not any voter's ideal point. There are many such mechanisms which are not dictatorial. However, if differentiability is required of the choice function, this forces it to be either constant or dictatorial. In the multidimensional case, non-separability of preferences leads to dictatorship, even if preferences are restricted to be quadratic.