Swarm intelligence is the decentralized process through which groups of social insects, such as swarms of bees, are able to coordinate their behavior, and make decisions collectively. This type of system resembles the structure of primate brains, and is organized in such a way that no individual agent possesses knowledge about all possible options. In spite of the bounded rationality of each of its components, this process is able to solve highly complex problems, such as foraging, migration, and labor organization. In particular, bee swarms exhibit exceptional promptness and accuracy in choosing new nesting sites – a well-documented best-of-N problem – despite relying exclusively on collective dynamics. Our goal is to analyze the emergence of collective decision-making, from simple individual behavioral rules. To that effect, we propose 3 cognitively plausible algorithms for social diffusion as applied to the nest-site selection process in the honeybee Apis mellifera. We then employ agent-based computer simulations and construct a mathematical model, in order to analyze the decisional properties of the corresponding emergent systems. We show that our model exhibits desirable properties for optimal decision-making, and predicts a number of empirical observations about nest-site selection in Apis mellifera. These findings give us insights into the dynamics of decentralized decision-making systems, and how advantageous collective properties can emerge from stereotyped individual rules.