Effects of network topology and trait distribution on collective decision making

Individual-level interactions shape societal or economic processes, such as infectious diseases spreading, stock prices fluctuating and public opinion shifting. Understanding how the interaction of different individuals affects collective outcomes is more important than ever, as the internet and social media develop. Social networks representing individuals' influence relations play a key role in understanding the connections between individual-level interactions and societal or economic outcomes. Recent research has revealed how the topology of a social network affects collective decision-making in a community. Furthermore, the traits of individuals that determine how they process received information for making decisions also change a community's collective decisions. In this work, we develop stochastic processes to generate networks of individuals with two simple traits: Being a conformist and being an anticonformist. We introduce a novel deterministic voter model for a trait-attributed network, where the individuals make binary choices following simple deterministic rules based on their traits. We show that the simple deterministic rules can drive unpredictable fluctuations of collective decisions which eventually become periodic. We study the effects of network topology and trait distribution on the first passage time for a sequence of collective decisions showing periodicity.