Towards Swarm Calculus: Universal Properties of Swarm Performance and Collective Decisions

The search for generally applicable methods in swarm intelligence aims to gain new insights about natural swarms and to develop design methodologies for artificial swarms. The ideal would be a ‘swarm calculus’ that allows to calculate key features such as expected swarm performance and robustness on the basis of a few parameters. A path towards this ideal is to find methods and models that have maximal generality. We report two models that might be examples of exceptional generality. First, we present an abstract model that describes the performance of a swarm depending on the swarm density based on the dichotomy between cooperation and interference. Second, we give an abstract model for decision making that is inspired by urn models. A parameter, that controls the feedback based on the current consensus, allows to understand the effects of an increasing probability for positive feedback over time in a decision making system.