How do Cockroach Groups Integrate Multiple Attributes in a Best-of-N Task?

Collective decision-making experiments have largely focused on simple scenarios in which groups choose between two options that differ along a single attribute. However, it remains unclear whether principles derived from this single-attribute best-of-2 paradigm generalizes to the multi-attribute, multi-option decisions that groups often face in nature. Here, we use mean-field and agent-based models of cockroach aggregation to study collective decision-making across a range of problem complexities, varying both the number of options (N) and the number of attributes describing each option. Our models make 3 novel predictions: (1) cockroach groups use a compensatory algorithm when integrating attributes, trading off strength in one attribute against weakness in another; (2) decision-making collapses abruptly once N exceeds a critical threshold; and (3) decision time scales non-monotonically with N. Together, these results indicate that dynamics characterized in single-attribute best-of-2 experiments do not extrapolate to multi-attribute best-of-N decision-making. Collective choice under realistic complexity may follow principles not yet captured by existing models.