Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation
Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation
复制标题
信念融合和话语困境：对判断聚合悖论的基于论证的解释
作者：
G. Pigozzi
将逻辑上相互关联的命题的个体判断聚合为对相同命题的集体决策称为判断聚合。社会选择和政治理论方面的文献声称，判断聚合引起了严重的关注。例如，考虑一组前提和一个结论，其中后者在逻辑上与前者等效。当多数投票应用于某些命题（前提）时，它可能会给出与应用于另一组命题（结论）的多数投票不同的结果。这个问题被称为话语困境（或悖论）。话语困境是一个严重的问题，因为尚不清楚这些情况下是否存在集体结果，如果存在，又会是什么样子。此外，正如我将要展示的那样，所建议的两种摆脱悖论的路线——所谓的基于前提的程序和基于结论的程序——并不是令人满意的群体决策方法。在本文中，我介绍了一种新的聚合过程，其灵感来自于人工智能中定义的运算符，用于合并信念基础。结果是，我们不需要担心自相矛盾的结果，因为只有当不排除不一致的集体判断从可能的解决方案中排除时，这些结果才会出现。
The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (the conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions.