Undecided Cliques Promote Consensus in the Directed Majority Automaton
Jake D. Christensen, David B. Griffin and David Peak
When fish that have been trained to school toward a blue or a yellow target are mixed together with only a small difference in population size they rarely change their target preference. When untrained fish are introduced, however, often the whole mixed population will school toward the target preferred by the initial majority. This is a macroscopic, biological example of the “majority identification problem” studied in the cellular automaton literature. By closely adhering to the empirical conditions of these experiments we have developed a “directed majority” cellular automaton that: (a) solves the identification problem well even for small initial majorities; (b) explains why untrained fish help persuade minority fish to join the majority; and (c) predicts that untrained fish achieve this feat by collaborating in spatially structured cliques that might be observable in experiments with larger populations. The directed majority automaton provides insight into the consensus forming process and holds promise for being able to predict when systems (similar to the fish) will successfully perform majority identification.
Keywords: Cellular automata; majority identification; consensus; clique