Optimal group composition for efficient division of labor

This study examines a group performing multiple tasks, with each subgroup performing each task expressed as a binary choice problem. Each subgroup uses the simple majority rule; a correct decision benefits the subgroup. This study demonstrates that, assuming all individuals' equal competence for all tasks and a sufficiently large group size, when each individual's probability of making a correct decision exceeds one-half, the optimal group composition is an equal number of individuals per subgroup. Conversely, it is less than one-half, the assignment produces the lowest benefit. We also find that when decision-making costs exist, if the competence is greater than one-half, the possibility that the performance of division of labor outweighs that of plenary voting increases as the cost increases. On the other hand, if the competence is less than one-half, division of labor is always more beneficial than plenary voting. The optimal group compositions for the cases where the group size is not sufficiently large are also discussed.