论文标题
在大多数规则下存在社会偏好传播和社会选择的定理的一个典范
A counter example to the theorems of social preference transitivity and social choice set existence under the majority rule
论文作者
论文摘要
我提供了一个例子，其中个人的偏好是严格的顺序，在大多数规则下，可以获得及物的社会秩序，因此也可以获得非空选择集。但是，该示例中个人的偏好并不满足Inada（1969）在多数统治下至少需要的任何条件（限制）。此外，被认为的个人的偏好不满足价值限制的条件（VR），极端限制（ER）或有限协议（LA），其中一些是Sen and Pattanaik（1969）所要求的，因为它是否存在非空的社会选择集。因此，该例子是大多数规则下的社会喜好传播和社会选择设定的许多定理的例外。该观察结果表明，Inada（1969）列出的条件的收集不像可能的那样完整。 Sen和Pattanaik（1969）考虑的条件，ER和LA的条件也是如此。这一观察结果是当前社会选择理论中某些必要条件的挑战。除了寻求新的条件外，应对这一挑战的一种可能方法是，从理论上的潜在性，可以根据常见的数学工具来代表已确定的条件（例如VR，ER和LA），然后人们可能会发现更多。
I present an example in which the individuals' preferences are strict orderings, and under the majority rule, a transitive social ordering can be obtained and thus a non-empty choice set can also be obtained. However, the individuals' preferences in that example do not satisfy any conditions (restrictions) of which at least one is required by Inada (1969) for social preference transitivity under the majority rule. Moreover, the considered individuals' preferences satisfy none of the conditions of value restriction (VR), extremal restriction (ER) or limited agreement (LA), some of which is required by Sen and Pattanaik (1969) for the existence of a non-empty social choice set. Therefore, the example is an exception to a number of theorems of social preference transitivity and social choice set existence under the majority rule. This observation indicates that the collection of the conditions listed by Inada (1969) is not as complete as might be supposed. This is also the case for the collection of conditions VR, ER and LA considered by Sen and Pattanaik (1969). This observation is a challenge to some necessary conditions in the current social choice theory. In addition to seeking new conditions, one possible way to deal with this challenge may be, from a theoretical prospective, to represent the identified conditions (such as the VR, ER and LA) in terms of a common mathematical tool, and then, people may find more.
