防级别策略的信念聚合机制
Level-strategyproof Belief Aggregation Mechanisms
摘要：
在集结专家对一个有序结果集的概率预测问题中，我们引入了水平策略证明公理（level-SP），并证明了它是一个自然的概念，有几个应用.此外，它是一个强大的概念，因为它意味着激励相容在一个丰富的域的单峰累积分布函数（CDF）的空间。这与文献相反，文献假设概率分布空间上的单峰偏好。我们的主要结果是：（1）将问题归结为CDF的聚集问题，（2）在加入和不加入其它公理的情况下，对水平SP概率聚集函数的公理化刻画，（3）为刻画提供界的不可能性结果，（4）对两种新的实用水平SP方法：比例累积法和中间最大累积法的公理化刻画，（5）对两种新的水平SP概率聚集函数的公理化刻画，（6）对两种新的水平SP概率聚集函数的公理化刻画，（7）对两种新的水平SP概率聚集函数的公理化刻画。以及（5）将比例累积法应用于将赞成投票、多数规则和多数判断方法扩展到选民/专家不确定如何对待排序的候选人/备选方案进行评级的情况。\footnote{We are grateful to Thomas Boyer-Kassem, Roger Cooke, Aris Filos-Ratsikas, Hervé Moulin, Clemens Puppe and some anonymous EC2021 referees for their helpful comments and suggestions.} \keywords{Probability Aggregation Functions \and ordered Set of Alternatives \and Level Strategy-Proofness \and Proportional-Cumulative \and Middlemost-Cumulative}
英文摘要：
In the problem of aggregating experts' probabilistic predictions over an ordered set of outcomes, we introduce the axiom of level-strategy\-proofness (level-SP) and prove that it is a natural notion with several applications. Moreover, it is a robust concept as it implies incentive compatibility in a rich domain of single-peakedness over the space of cumulative distribution functions (CDFs). This contrasts with the literature which assumes single-peaked preferences over the space of probability distributions. Our main results are: (1) a reduction of our problem to the aggregation of CDFs; (2) the axiomatic characterization of level-SP probability aggregation functions with and without the addition of other axioms; (3) impossibility results which provide bounds for our characterization; (4) the axiomatic characterization of two new and practical level-SP methods: the proportional-cumulative method and the middlemost-cumulative method; and (5) the application of proportional-cumulative to extend approval voting, majority rule, and majority judgment methods to situations where voters/experts are uncertain about how to grade the candidates/alternatives to be ranked.\footnote{We are grateful to Thomas Boyer-Kassem, Roger Cooke, Aris Filos-Ratsikas, Hervé Moulin, Clemens Puppe and some anonymous EC2021 referees for their helpful comments and suggestions.} \keywords{Probability Aggregation Functions \and ordered Set of Alternatives \and Level Strategy-Proofness \and Proportional-Cumulative \and Middlemost-Cumulative}
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
