To Lead or to be Led: A Generalized Condorcet Jury Theorem under Dependence

A talk by Jonas Karge:
June 29, 2023
11 a.m. – noon
TU Dresden, APB/3027 | BigBlueButton
Join us now: https://bbb.tu-dresden.de/b/pio-zwt-smp-aus
https://iccl.inf.tu-dresden.de/web/To_Lead_or_to_be_Led:_A_Generalized_Condorcet_Jury_Theorem_under_Dependence

Abstract

Aggregating pieces of information or beliefs held by (abstract) agents is central to a variety of belief merging applications. When the merging process aims at retrieving an underlying ground truth, the Condorcet Jury Theorem (CJT) allows identifying voting rules that almost surely track the true piece of information for large groups of agents, given that specific conditions are met. As essential assumptions, the CJT relies on all agents being equally competent as well as independent from one another. In the search for a generalization of the CJT applicable to real-world scenarios, both aforementioned assumptions were weakened separately. In this work, we provide a generalization of the CJT that allows, at the same time, for heterogeneous competence levels across agents as well as a degree of dependence modeled through an opinion leader exerting influence on the electorate. Additionally, we derive a concrete bound on the number of agents necessary to successfully track the underlying ground truth, and examine the bound's tightness by means of statistical simulations.