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 , where represents the ratio of asymmetric voting noise. Remarkably, even in scenarios with extreme voting asymmetry (), 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 , 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.