The ability of a honeybee swarm to select the best nest site plays a fundamental role in determining the future colony's fitness. To date, the nest-site selection process has mostly been modeled and theoretically analyzed for the case of binary decisions. However, when the number of alternative nests is larger than two, the decision-process dynamics qualitatively change. In this work, we extend previous analyses of a value-sensitive decision-making mechanism to a decision process among N nests. First, we present the decision-making dynamics in the symmetric case of N equal-quality nests. Then, we generalize our findings to a best-of-N decision scenario with one superior nest and N - 1 inferior nests, previously studied empirically in bees and ants. Whereas previous binary models highlighted the crucial role of inhibitory stop-signaling, the key parameter in our new analysis is the relative time invested by swarm members in individual discovery and in signaling behaviors. Our new analysis reveals conflicting pressures on this ratio in symmetric and best-of-N decisions, which could be solved through a time-dependent signaling strategy. Additionally, our analysis suggests how ecological factors determining the density of suitable nest sites may have led to selective pressures for an optimal stable signaling ratio.
