Multi-Agent Belief Management

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Multi-Agent Belief Management

Vortrag von Jonas Karge
How can groups of imperfect and uncertain agents arrive at reliable collective judgments? This talk approaches this question through the Condorcet Jury Theorem, which formalizes the wisdom-of-the-crowds effect under idealized assumptions.

The first part asks when a group can be expected to identify a correct alternative through voting. After introducing the classical theorem, the speaker will present a generalization to approval voting with multiple alternatives, heterogeneous competence levels, and dependence induced by an opinion leader. The resulting framework provides finite-sample and asymptotic guarantees for collective truth tracking. It is then applied to the comparison between diversity and ability, deriving a threshold that specifies when reduced dependence can compensate for lower competence. The second part asks how uncertain beliefs can be aggregated reliably. The talk introduces Voting for Bins, a method in which interval-valued probabilistic beliefs are transformed into votes over probability intervals. The generalized jury-theorem guarantees then provide bounds on both the correctness and precision of the collective belief. This framework is used to analyze when adding an opinion leads to dilation or contraction of the pooled interval. Finally, the speaker will outline how the same epistemic approach can be extended from probability intervals to the aggregation of numerical estimates.


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