Econ Papers Daily / 期刊论文
阿罗独立性公理与选择函数的加总
Arrovian independence and the aggregation of choice functions
摘要
We reappraise the Arrow problem by studying the aggregation of choice functions. We do so in the general framework of judgment aggregation, in which choice functions are naturally representable by specifying, for each menu A and each alternative x in A , whether x is choosable from A , or not. Our framework suggests a natural strengthening of Arrow’s independence condition positing that the collective choosability of an alternative from a menu depends on the individual views on that issue, and that issue alone. Our analysis reveals that Arrovian impossibility results crucially hinge on what internal consistency requirements we impose on choice functions. While the aggregation of ‘binary’ choice functions, i.e.those satisfying both contraction (\(\alpha \)) and expansion (\(\gamma \)) consistency, is necessarily dictatorial, possibilities in the form of oligarchic rules emerge for path-independent choice functions, that is, when the expansion property \(\gamma \) is replaced by the so-called Aizerman condition. Remarkably, the Arrovian aggregation of choice functions is shown to be almost dictatorial already under property \(\gamma \) alone. When giving up expansion consistency, specific quota rules become possible.
中文摘要
我们通过研究选择函数的加总问题，重新审视了阿罗悖论。在判断加总的通用框架下，选择函数可自然地表示为：针对每个菜单A及其中的每个备选项x，明确x是否可从A中被选出。该框架提出了对阿罗独立性条件的自然强化，即集体对某备选项从某菜单中的可选择性，仅取决于个体对该议题的判断，且仅取决于该议题本身。分析表明，阿罗式不可能性结果的关键在于我们对选择函数施加何种内部一致性要求。当加总满足收缩一致性（\(\alpha\)）与扩张一致性（\(\gamma\)）的"二元"选择函数时，结果必然具有独裁性；而对于路径独立型选择函数（即用所谓的艾泽曼条件替代扩张性质\(\gamma\)），则可能出现寡头规则形式的可能性。值得注意的是，仅凭性质\(\gamma\)，阿罗式选择函数加总已近乎呈现独裁特征。若放弃扩张一致性，则特定配额规则成为可能。