Collective decision-making enables multi-robot systems to act autonomously in real-world environments. Existing collective decision-making mechanisms suffer from the so-called speed versus accuracy trade-off or rely on high complexity, e.g., by including global communication. Recent work has shown that more efficient collective decision-making mechanisms based on artificial neural networks can be generated using methods from evolutionary computation. A major drawback of these decision-making neural networks is their limited interpretability. Analyzing evolved decision-making mechanisms can help us improve the efficiency of hand-coded decision-making mechanisms while maintaining a higher interpretability. In this paper, we analyze evolved collective decision-making mechanisms in detail and hand-code two new decision-making mechanisms based on the insights gained. In benchmark experiments, we show that the newly implemented collective decision-making mechanisms are more efficient than the state-of-the-art collective decision-making mechanisms voter model and majority rule.