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

TL;DR

This paper introduces two highly general models for swarm intelligence: one for performance based on cooperation and interference, and another for collective decision making inspired by urn models, aiming to develop a universal swarm calculus.

Contribution

It presents two abstract models with broad applicability for understanding swarm performance and decision processes, advancing towards a universal swarm calculus.

Findings

Model fits various swarm experiment results

Urn-inspired decision model captures positive feedback effects

Methods like Markov processes and first passage times are applicable

Abstract

Methods of general applicability are searched for in swarm intelligence with the aim of gaining new insights about natural swarms and to develop design methodologies for artificial swarms. An ideal solution could be a `swarm calculus' that allows to calculate key features of swarms such as expected swarm performance and robustness based on only a few parameters. To work towards this ideal, one needs to find methods and models with high degrees of generality. In this paper, we report two models that might be examples of exceptional generality. First, an abstract model is presented that describes swarm performance depending on swarm density based on the dichotomy between cooperation and interference. Typical swarm experiments are given as examples to show how the model fits to several different results. Second, we give an abstract model of collective decision making that is inspired by urn models. The effects of positive feedback probability, that is increasing over time in a decision making system, are understood by the help of a parameter that controls the feedback based on the swarm's current consensus. Several applicable methods, such as the description as Markov process, calculation of splitting probabilities, mean first passage times, and measurements of positive feedback, are discussed and applications to artificial and natural swarms are reported.