Condorcet and Beyond: An Empirical Comparison of Voting Rules

Area of Science:

• Social Psychology
• Decision Science
• Collective Intelligence

Background:

• The Condorcet Jury Hypothesis posits that majority voting improves accuracy over individual judgments.
• Translating probabilistic judgments into categorical beliefs is crucial for group decision-making.

Purpose of the Study:

• To evaluate the performance of various voting and probability aggregation methods.
• To investigate the accuracy-decisiveness trade-offs inherent in different collective decision-making strategies.
• To compare the efficacy of methods like majority, unanimity, and probability averaging.

Main Methods:

• Analysis of 451,200 probability judgments from 376 participants on 1200 general knowledge claims.
• Comparison of six aggregation methods: majority, strict majority, unanimity, strict unanimity, probability averaging, and log-odds averaging.
• Application of Locke's Thesis to convert probabilistic judgments into categorical beliefs.

Main Results:

• All methods exhibit accuracy-decisiveness trade-offs.
• Majority voting offers high decisiveness but moderate accuracy.
• Probability aggregation methods generally provide the best balance between accuracy and decisiveness.
• Strict majority voting is frequently outperformed by other methods in both accuracy and decisiveness.
• Increased judgment diversity correlates with higher group accuracy.

Conclusions:

• Probability aggregation methods are often superior to simple voting rules for group decision-making.
• Strict majority voting, despite its prevalence, may not be the optimal strategy for maximizing group accuracy and decisiveness.
• Encouraging diversity in individual judgments can enhance overall group accuracy.