Group decisions based on confidence weighted majority voting

Sascha Meyen,Dorothee M B Sigg,Ulrike Von Luxburg,Volker H Franz

doi:10.1186/s41235-021-00279-0

Abstract

BackgroundIt has repeatedly been reported that, when making decisions under uncertainty, groups outperform individuals. Real groups are often replaced by simulated groups: Instead of performing an actual group discussion, individual responses are aggregated by a numerical computation. While studies have typically used unweighted majority voting (MV) for this aggregation, the theoretically optimal method is confidence weighted majority voting (CWMV)—if independent and accurate confidence ratings from the individual group members are available. To determine which simulations (MV vs. CWMV) reflect real group processes better, we applied formal cognitive modeling and compared simulated group responses to real group responses.ResultsSimulated group decisions based on CWMV matched the accuracy of real group decisions, while simulated group decisions based on MV showed lower accuracy. CWMV predicted the confidence that groups put into their group decisions well. However, real groups treated individual votes to some extent more equally weighted than suggested by CWMV. Additionally, real groups tend to put lower confidence into their decisions compared to CWMV simulations.ConclusionOur results highlight the importance of taking individual confidences into account when simulating group decisions: We found that real groups can aggregate individual confidences in a way that matches statistical aggregations given by CWMV to some extent. This implies that research using simulated group decisions should use CWMV instead of MV as a benchmark to compare real groups to.

Highlights

It has repeatedly been reported that, when making decisions under uncertainty, groups outperform individuals
We introduce the parameter β to estimate the equality effect capturing whether real groups weighted individual responses in a way that deviates from confidence weighted majority voting (CWMV)
We conducted two-sided, exact binomial tests to confirm this pattern: majority voting (MV) simulations were less accurate than CWMV simulations ( p = 0.016 ) and real group decisions ( p = 0.016)

Summary

Introduction

It has repeatedly been reported that, when making decisions under uncertainty, groups outperform individuals. Some of the above-mentioned studies used real groups (Hautz et al 2015; Klein and Epley 2015; van Dijk et al 2014), all of these studies simulated group decisions: Individuals gave responses that were statistically aggregated into one simulated group response without a real group discussion occurring. One frequently used method is majority voting (MV; Hastie and Kameda 2005; and see for example Klein and Epley 2015; van Dijk et al 2014; Kosinski et al 2012; Kurvers et al 2016; Sorkin et al 2001)

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