Remarks on the Theory of Collective Choice
Remarks on the Theory of Collective Choice
复制标题
集体选择理论评述
作者：
K. Suzumura
自从阿罗（1963）将所谓的投票悖论推广到集体决策的每一种民主方法以来，出现了大量文献（a）试图通过削弱阿罗的某些条件来规避他的困难（Bordes，1976; Hansson，1973; Plott，1973; Sen，1969）;（B）提出集体选择理论中的一些其他悖论（Batra and Pattanaik，1972; Hansson，1969; Schwartz，1970; Sen，1970 a）和（c）质疑阿罗定理与帕累托福利经济学理论的相关性（Bergson，1966; Little，1952; Samuelson，1967，1977）。本文的目的是对集体选择理论的这些最新发展发表一些评论。本文的第一部分讨论的问题是，为了避免阿罗的不可能性结果，人们需要在多大程度上削弱阿罗的集体理性条件。众所周知，阿罗（Arrow，1963）提出了集体理性条件，即社会可以按照偏好顺序排列所有可能的备选方案，如果指定了某个可用的备选方案集，社会必须从中选择与该偏好顺序相关的最佳备选方案。我们将考虑比阿罗的条件弱的两个相容选择条件。第一个条件要求，如果在二元选择中选择了一个替代品x而不是另一个替代品y，那么y永远不应该从包含x的任何替代品集合中选择;而第二个条件要求，如果在二元选择中选择了x而不是y，那么不存在选择y并且x可用但被拒绝的选择情况。(In如果还选择了x，则可以选择第二种情况y，而在第一种情况下，无论如何不能选择y。在这两个看似相似的一致性条件之间，似乎有一条鸿沟将可能性与不可能性分开。它将表明，第一个一致性要求是incompatible与本质上Arrovian条件的集体选择规则，而第二个一致性条件是兼容的相同的条件。虽然这些一致性要求之间的差异非常微妙，但其在不可能结果的背景下的含义因此截然不同。为了避免我们过于满意，我们必须赶紧补充说，没有一个满足我们第二个一致性要求的集体选择规则能够摆脱帕累托自由主义悖论（Sen，1970 a; Batra and Pattanaik，1972）。阿罗-森理论，然后与柏格森-萨缪尔森一个对比。考虑到这一点，我们可以很方便地记住阿罗关于集体选择规则的不相容条件可以分为两类。第一类是适用于个人偏好关系的任何固定轮廓的陈述，而第二类是指集体选择对轮廓变化的反应。(The第一类包括集体理性和帕累托规则的条件，而第二类包括无关选项的独立性
Ever since the so-called paradox of voting was generalized by Arrow (1963) to every democratic method of collective decision-making, a vast literature has appeared (a) trying to circumvent Arrow's difficulty by weakening some of his conditions (Bordes, 1976; Hansson, 1973; Plott, 1973; Sen, 1969); (b) proposing some other paradoxes in the theory of collective choice (Batra and Pattanaik, 1972; Hansson, 1969; Schwartz, 1970; Sen, 1970a) and (c) casting doubts about the relevance of Arrow's theorem to the theory of Paretian welfare economics (Bergson, 1966; Little, 1952; Samuelson, 1967, 1977). The purpose of this paper is to make some remarks on these recent developments in the theory of collective choice. The first part of the paper deals with the question of how much one needs to weaken Arrow's collective rationality condition in order to avoid his impossibility result. As is well known, Arrow (1963) imposed the collective rationality condition that the society can arrange all conceivable alternatives in order of preference and that, if some available set of alternatives is specified, the society must choose therefrom the best alternative with respect to that preference ordering. We will consider two conditions of consistent choice which are weaker than that of Arrow. The first condition requires that, if an alternative x is chosen over another alternative y in binary choice, y should never be chosen from any set of alternatives that contain x; while the second condition requires that, if x is chosen over y in binary choice, there exists no choice situation in which y is chosen and x is available but rejected. (In the second case y can be chosen if x is also chosen, while in the first case y cannot be chosen anyway.) There seems to be a gulf that separates possibility from impossibility in between these two seemingly similar consistency conditions. It will be shown that the first consistency requirement is incomnpatible with essentially Arrovian conditions on the collective choice rule, while the second consistency condition is compatible with the same conditions. Although the difference between these consistency requirements is very subtle, the implication thereof in the context of impossibility result is therefore dramatically different. Lest we should be too satisfied, we must hasten to add that no collective choice rule satisfying our second consistency requirement can be free from the paradox of Paretian liberal (Sen, 1970a; Batra and Pattanaik, 1972). The Arrow-Sen theory is then contrasted with the Bergson-Samuelson one. In view of doing this, it is convenient to remember that Arrow's incompatible conditions on collective choice rule can be classified into two categories. The first category consists of statements that apply to any fixed profile of individual preference relations, while the second category refers to the responsiveness of the collective choice to the variations in profiles. (The first category embraces the condition of collective rationality and the Pareto rule, while the second category consists of the independence of irrelevant alternatives