A design pattern for best-of-n collective decisions

The engineering of large-scale decentralised systems requires sound methodologies to guarantee the attainment of the desired macroscopic system-level behaviour given the microscopic individual-level implementation. While a general-purpose methodology is currently out of reach, specific solutions can be given to broad classes of problems by means of well-conceived design patterns, which recall the well-known concept exploited in software engineering [1]. Design patterns provide formal guidelines to deal with recurring problems in a specific domain. For the particular case of distributed systems, design patterns should prescribe the individual-level microscopic behaviour required to obtain desired system-level macroscopic properties [2, 3]. Here, we present a design pattern for decentralised decision-making—a fundamental ability in several contexts and application domains [4, 5, 6]. The design pattern is based on the nest-site selection behaviour of honeybee swarms [7, 8, 9]. Previous experimental and theoretical studies have demonstrated near-optimal speed-accuracy tradeoffs in the selection of the most profitable option among a set of alternative nesting sites by honeybees [7, 8]. Most importantly, inhibitory signals among bees provide an adaptive mechanism to quickly break deadlocks and tune the decision dynamics according to the perceived quality of the discovered options [8, 9]. The above properties of the nest-site selection process are relevant for many practical decisionmaking scenarios in decentralised systems. Starting from the macroscopic description of the nest-site selection dynamics [8, 9], we derive the exact relationship between microscopic and macroscopic models—also including finite-size effects—for the general case of a best-of-n decision problem. The inter-related models represent the core of the design pattern, which is completed by formal guidelines for the implementation of collective decisions in multiagent systems. We provide guidelines for implementation by means of either homogenous or heterogeneous agents, as well as guidelines for the inclusion of spatial and topological factors that have a bearing in determining the microscopic interaction patterns. We report here a case study that illustrates the application of the design pattern, and we briefly discuss the results obtained in other case studies, as well as the relevance of the obtained results for better understanding the behaviour of natural systems.