Group cohesion under asymmetric voting behaviors

TL;DR

This paper investigates how asymmetric voting behaviors influence group cohesion, revealing that cohesion can be maintained even with extreme asymmetry and identifying critical factors like attention decay and group size.

Contribution

It extends previous models by incorporating asymmetric voting noise and analyzes their effects on group cohesion through theoretical and simulation methods.

Findings

Group cohesion converges to 1/(R+1) as group size approaches infinity.

High voting asymmetry (R→∞) still allows for significant cohesion.

Attention decay rate impacts cohesion near phase transition points.

Abstract

Cohesion plays a crucial role in achieving collective goals, promoting cooperation and trust, and improving efficiency within social groups. To gain deeper insights into the dynamics of group cohesion, we have extended our previous model of noisy group formation by incorporating asymmetric voting behaviors. Through a combination of theoretical analysis and numerical simulations, we have explored the impact of asymmetric voting noise, the attention decay rate, voter selection methods, and group sizes on group cohesion. For a single voter, we discovered that as the group size approaches infinity, group cohesion converges to $1/(R+1)$, where $R$ represents the ratio of asymmetric voting noise. Remarkably, even in scenarios with extreme voting asymmetry ($R \to \infty$), a significant level of group cohesion can be maintained. Furthermore, when the positive or negative voter's voting noise surpasses or falls below the phase transition point of $R_c=1$, a higher rate of attention decay can lead to increased group cohesion. In the case of multiple voters, a similar phenomenon arises when the attention decay rate reaches a critical point. These insights provide practical implications for fostering effective collaboration and teamwork within growing groups striving to achieve shared objectives.