Epistemic Democracy: Generalizing the Condorcet Jury Theorem

List, Christian; Goodin, Robert E.

doi:10.1111/1467-9760.00128

Cited by 415 publications

(224 citation statements)

References 31 publications

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“…The P best of the teams is higher than the P best of each one of the agents, and is higher for a team of 6 agents than for a team of 4 agents. This result is expected when we consider the extended version of the Condorcet's Jury Theorem [2], at least for a uniform team. According to the theorem P best approaches 1 when the number of agents goes to infinity.…”

Section: Experiments In Computer Gomentioning

confidence: 68%

“…According to the theorem, when facing a binary decision, as long as the average of the probability of each individual being correct is higher than 1 2 , a group of independent individuals doing plurality voting will have a higher probability of being correct than the individuals alone. This theorem is extended to the k options case in [2], where it is shown that if each of the individuals have a probability of choosing the best answer higher than choosing any other answer, the group performing plurality voting will be stronger than the individuals alone. These theorems, however, do not present any benefits in having diverse agents.…”

Section: Related Workmentioning

confidence: 99%

“…Voting is an important coordination mechanism for a multi-agent team. By voting, we can use agents that were not originally designed to work together, and there are theoretical guarantees that a team of voting agents can get closer to finding the best possible decision in a given situation [2]. Sometimes the agents must vote continuously in many different scenarios.…”

Section: Introductionmentioning

confidence: 99%

“…When a team votes to decide its final opinion, their model and theorems do not hold anymore. In the current literature on voting it is assumed a model where agents have a fixed probability to take the best action [7,2,[8][9][10], and under that model it is not possible to show any advantage in having a diverse team of agents. Our experiments show, however, that a diverse team can outperform a uniform team of stronger agents.…”

Section: Introductionmentioning

confidence: 99%

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A Detailed Analysis of a Multi-agent Diverse Team

Marcolino

Zhang

Jiang

et al. 2014

Coordination, Organizations, Institutions, and Norms in Agent Systems IX

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Abstract.In an open system we can have many different kinds of agents. However, it is a challenge to decide which agents to pick when forming multi-agent teams. In some scenarios, agents coordinate by voting continuously. When forming such teams, should we focus on the diversity of the team or on the strength of each member? Can a team of diverse (and weak) agents outperform a uniform team of strong agents? We propose a new model to address these questions. Our key contributions include: (i) we show that a diverse team can overcome a uniform team and we give the necessary conditions for it to happen; (ii) we present optimal voting rules for a diverse team; (iii) we perform synthetic experiments that demonstrate that both diversity and strength contribute to the performance of a team; (iv) we show experiments that demonstrate the usefulness of our model in one of the most difficult challenges for Artificial Intelligence: Computer Go 1 .

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Section: Experiments In Computer Gomentioning

confidence: 68%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Detailed Analysis of a Multi-agent Diverse Team

Marcolino

Zhang

Jiang

et al. 2014

Coordination, Organizations, Institutions, and Norms in Agent Systems IX

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“…In a system of voting agents, however, disagreements are inherent in the coordination process and do not necessarily mean that an erroneous situation has occurred due to such malfunction. Additionally, research in social choice is mostly focused on studying the guarantees of finding the optimal choice given a noise model for the agents and a voting rule [14,19,49], but provide no help in assessing the performance of a team of voting agents.…”

Section: Introductionmentioning

confidence: 99%

Every team deserves a second chance: an extended study on predicting team performance

Marcolino

Lakshminarayanan

Nagarajan

et al. 2016

Auton Agent Multi-Agent Syst

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Voting among different agents is a powerful tool in problem solving, and it has been widely applied to improve the performance in finding the correct answer to complex problems. We present a novel benefit of voting, that has not been observed before: we can use the voting patterns to assess the performance of a team and predict their final outcome. This prediction can be executed at any moment during problem-solving and it is completely domain independent. Hence, it can be used to identify when a team is failing, allowing an operator to take remedial procedures (such as changing team members, the voting rule, or increasing the allocation of resources). We present three main theoretical results: (1) we show a theoretical explanation of why our prediction method works; (2) contrary to what would be expected based on a simpler explanation using classical voting models, we show that we can make accurate predictions irrespective of the strength (i.e., performance) of the teams, and that in fact, the prediction can work better for diverse teams composed of different agents than uniform teams made of copies of the best agent; (3) we show that the quality of our prediction increases with the size of the action space. We perform extensive experimentation in two different domains: Computer Go and Ensemble Learning. In Computer Go, we obtain high Multi-Agent Syst (2017) 31:1003-1054 quality predictions about the final outcome of games. We analyze the prediction accuracy for three different teams with different levels of diversity and strength, and show that the prediction works significantly better for a diverse team. Additionally, we show that our method still works well when trained with games against one adversary, but tested with games against another, showing the generality of the learned functions. Moreover, we evaluate four different board sizes, and experimentally confirm better predictions in larger board sizes. We analyze in detail the learned prediction functions, and how they change according to each team and action space size. In order to show that our method is domain independent, we also present results in Ensemble Learning, where we make online predictions about the performance of a team of classifiers, while they are voting to classify sets of items. We study a set of classical classification algorithms from machine learning, in a data-set of hand-written digits, and we are able to make high-quality predictions about the final performance of two different teams. Since our approach is domain independent, it can be easily applied to a variety of other domains.

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