Dictatorial domains in preference aggregation
Dictatorial domains in preference aggregation
复制标题
偏好聚合中的独裁域
DOI：
10.1007/s00355-006-0154-7
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发表时间：
2006
影响因子：
0.9
通讯作者：
M. Sanver
中科院分区：
文献类型：
--
作者：
U. Ozdemir;M. Sanver
如果不存在阿罗维（帕累托最优，IIA和非独裁）社会福利函数，我们称偏好排序领域为“独裁”。在一个有限的选择世界中，排除了冷漠，我们确定了一个条件，暗示了一个领域的专政性。这种情况，我们称之为“基本饱和”，是相当弱的。事实上，与选择的数量无关，存在一个本质上饱和的（因此是独裁的）领域，它由精确的六种排序组成。而且，该域还具有上专政性，即它的每一个超域都是专政的。因此，给定替代方案，监督域的大小与完整域的大小之比可能小至6/m！，随着增量收敛于零。
We call a domain of preference orderings “dictatorial” if there exists no Arrovian (Pareto optimal, IIA and non-dictatorial) social welfare function defined over that domain. In a finite world of alternatives where indifferences are ruled out, we identify a condition which implies the dictatoriality of a domain. This condition, to which we refer as “being essentially saturated”, is fairly weak. In fact, independent of the number of alternatives, there exists an essentially saturated (hence dictatorial) domain which consists of precisely six orderings. Moreover, this domain exhibits the superdictatoriality property, i.e., every superdomain of it is also dictatorial. Thus, givenmalternatives, the ratio of the size of a superdictatorial domain to the size of the full domain may be as small as 6/m!, converging to zero asmincreases.