Determining the optimal choice among multiple options is necessary in various situations, and the collective rationality of groups has recently become a major topic of interest. Social insects are thought to make such optimal choices by collecting individuals' responses relating to an option's value (=a quality-graded response). However, this behaviour cannot explain the collective rationality of brains because neurons can make only ‘yes/no’ responses on the basis of the response threshold. Here, we elucidate the basic mechanism underlying the collective rationality of such simple units and show that an ant species uses this mechanism. A larger number of units respond ‘yes’ to the best option available to a collective decision-maker using only the yes/no mechanism; thus, the best option is always selected by majority decision. Colonies of the ant Myrmica kotokui preferred the better option in a binary choice experiment. The preference of a colony was demonstrated by the workers, which exhibited variable thresholds between two options' qualities. Our results demonstrate how a collective decision-maker comprising simple yes/no judgement units achieves collective rationality without using quality-graded responses. This mechanism has broad applicability to collective decision-making in brain neurons, swarm robotics and human societies.

Benefits of grouping, not the Hamilton’s relatedness asymmetry benefit, mainly drive the evolution of eusociality in a bee.