From different angles of science, there has been a growing interest in the abilities of groups to track the truth. The Condorcet Jury Theorem (1785) states that without communication, infinitely big groups will reach a correct majority opinion with certainty. Coughlan (2000), meanwhile formulated a model in which all agents communicate with each other, showing that majorities are only just as good as fully-communicating individuals. In reality, communication is usually between these two extremes: some agents communicate with some of the (...) others, but not with all others. We refer to this as partial communication. This thesis provides a Bayesian framework to study the influence of partial communication on individual as well as group accuracy, thereby generalising Condorcet’s as well as Coughlan’s setting. We obtain results for individual and group accuracy in three type of networks. Firstly, we study the extreme case where there is either no communication or everyone communicates with everyone. Secondly, we determine accuracy for regular networks, in which all agents communicate with equally many other agents. Thirdly, we derive a formula to express the expected accuracy in random networks, in which agents can communicate with various numbers of other agents. The formula enables us to determine the effect of various parameters on the individual and group accuracy in a random network with partial communication. Finally, we show that in random networks, despite correlation between agents, we can still obtain accurate majorities under some constraints. (shrink)

Does pre-voting group deliberation improve majority outcomes? To address this question, we develop a probabilistic model of opinion formation and deliberation. Two new jury theorems, one pre-deliberation and one post-deliberation, suggest that deliberation is beneficial. Successful deliberation mitigates three voting failures: (1) overcounting widespread evidence, (2) neglecting evidential inequality, and (3) neglecting evidential complementarity. Formal results and simulations confirm this. But we identify four systematic exceptions where deliberation reduces majority competence, always by increasing Failure 1. Our analysis recommends deliberation that (...) is 'participatory', 'neutral', but not necessarily 'equal', i.e., that involves substantive sharing, privileges no evidences, but might privilege some persons. (shrink)

According to the skeptical argument from disagreement, we are mandated to suspend judgement about a question if we discover that others disagree with us. Critics, however, have proposed that this skeptical argument fails if there are not equally many people on either side of the debate: numbers matter. The present paper explicates this as the argument that a group can be more likely to arrive at the correct view by majority rule than the members are on their own. Defenders of (...) the skeptical argument have resisted that numbers matter by observing that if group members depend on each other when forming their beliefs, then the group can be less competent than its members. However, neither side of the debate has accompanied their views with quantitative estimates of how detrimental dependence is for group competence. This paper tries to improve this situation by drawing on jury theorems from social choice theory. The paper cannot settle the debate, but it shows that even the lower limit on group competence will exceed the average individual competence when dependence among voters remains moderate. This should give confidence to those who propose that asymmetry between the disputing parties can counter the skeptical argument from disagreement since being in the majority can thus be higher-order evidence for the disputed proposition. (shrink)

This paper studies the three kinds of conservativeness in a jury decision-making structure: the voting rule, the threshold of reasonable doubt, and the legal information system. In a model of simultaneous voting, Feddersen and Pesendorfer (The American Political Science Review, 92(1), 23-35, 1998) argue that the unanimity rule is the worst-performing voting rule because voters with strategic behaviour mitigate the bias brought about by the voting rule. If this bias can be offset by an opposing (less conservative) bias in the (...) legal information system, we would be able to restore the rationality of informative voting. The new informative equilibrium is strictly better than the original strategic equilibrium in terms of ex post error probability. When a strategic equilibrium survives, we can lower the probability of convicted defendant being innocent by making the information system more informative or by forming a jury with a higher (more conservative) threshold of reasonable doubt. (shrink)