Generalizations of Condorcet's Jury Theorem

社会和组织花费了大量的资源来寻找真相或确定世界的真实状态。例如，它必须决定被告是否有罪，经济是否处于衰退，或者一块给定的土地是否有石油。通常，决定是在相对无知的状态下做出的，因为没有人知道真相。那么问题来了：社会应该以什么规则来决定？特别是，社会是否更有可能通过将发现任务委托给其成员之一或遵循多数原则投票的陪审团（委员会）来成功？如果是后者，谁应该是陪审团成员？当选择的数量是两个时，孔多塞的陪审团定理（CJT）指出，在某些条件下，大多数陪审员会比任何一个人做得更好。不幸的是，这些条件很难满足：CJT假设陪审员(i)有共同的目标，（ii）独立投票。在现实中，假设(i)可能不满足，而假设（ii）很少满足。本研究旨在从多个方向推进孔多塞的陪审定理。它通过同时允许利益冲突和相关投票来综合前面关于CJT的工作。它研究的选择情境中，选择不是固定的，而是由选民之间的互动产生的。特别是，这项研究试图具体说明，在何种条件下，相对不了解情况的选民能够在掌握充分信息的情况下获得他们所选择的结果。

Societies and organizations spend considerable resources in search of the truth or to identify the true state of the world. For example, it must be decided whether a defendant is guilty, an economy is in recession or a given parcel of land bears oil. Usually, the decision is made in a state of relative ignorance because no one knows the truth. The question then arises: By what rule should the society decide? In particular, is the society more likely to succeed by delegating the task of discovery to one of its members or to a jury (committee) which follows majority-rule voting? If the latter, who should be on the jury? When the number of alternatives is two, Condorcet's jury theorem (CJT) states that under certain conditions a majority of jurors would do better than any one individual. Unfortunately, these conditions are difficult to satisfy: CJT assumes that jurors (i) share a common goal, and (ii) vote independently. In reality, assumption (i) may not be met, and assumption (ii) is seldom met. This research investigation seeks to advance Condorcet's jury theorem in various directions. It synthesizes the preceding work on CJT by permitting simultaneously both conflict of interest and correlated votes. It studies choice situations where the alternatives are not fixed but arise from interactions among the voters. In particular, the research seeks to specify conditions under which a relatively uninformed electorate attains the outcome it would choose with full information.