Collective decision-making under changing social environments among agents adapted to sparse connectivity

Abstract

Humans and other animals often follow the decisions made by others because these are indicative of the quality of possible choices, resulting in ‘social response rules’, that is, observed relationships between the probability that an agent will make a specific choice and the decisions other individuals have made. The form of social responses can be understood by considering the behaviour of rational agents that seek to maximise their expected utility using both social and private information. Previous derivations of social responses assume that agents observe all others within a group, but real interaction networks are often characterised by sparse connectivity. Here, I analyse the observable behaviour of rational agents that attend to the decisions made by a subset of others in the group. This reveals an adaptive strategy in sparsely connected networks based on highly simplified social information, that is, the difference in the observed number of agents choosing each option. Where agents employ this strategy, collective outcomes and decision-making efficacy are controlled by the social connectivity at the time of the decision, rather than that to which the agents are accustomed, providing an important caveat for sociality observed in the laboratory and suggesting a basis for the social dynamics of highly connected online communities.

Collective decision strategies in the presence of spatio-temporal correlations

“…In particular, spatial correlation can break the “wisdom of crowds” effect (higher collective accuracy with increasing group size) and lead to accuracy being maximized at relatively small group sizes. Similar effects can be observed when correlations are produced via social influence within the group itself, rather than being a property of external cues (Mann, 2021; Vicente-Page et al, 2018). Some recent studies have demonstrated ways in which groups might overcome the impact of spatially correlated information on collective decision-making, including utilizing stalemates (Winklmayr et al, 2020) or creating internal structure within the group (Kao and Couzin, 2019).…”

Agents seeking long-term access to the wisdom of the crowd reduce immediate decision-making accuracy

“…The Condorcet Jury Theorem (CJT) states that if agents individually make independent choices with some accuracy greater than 0.5, the probability that the majority of the group chooses correctly rapidly approaches one. However, the assumption of independent decision-making in the CJT is already violated when rational agents choose sequentially, and further biases towards consensus tend to further decrease the accuracy of the majority decision [18]. To examine how the bias towards consensus induced by future-weighting affects collective wisdom, I calculated the probability of all decision sequences in a group of 15 agents for cases where the correct option was A ( x = 1) or B ( x = − 1), varying the future-weighting in the form of the expected number of future games (1 / (1 − γ )).…”

“…Maximising this expectation with respect to Δ ∗ provides the optimal threshold value, which matches that derived in ref. [19].…”

“…The use of social information in decision-making can be understood as an adaptive behaviour that maximises fitness by enabling an animal to choose behaviours with the highest expected reward, whether through an explicitly cognitive process or via heuristic ‘rules of interaction’ – ingrained, evolutionarily-selected tendencies to copy what others do under certain condition or consistent weightings of social and non-social information [8]. Following this logic, previous research has sought to derive these rules of behaviour from first principles, by considering what a rational agent would do given the social and non-social information available when faced with a decision between different options with uncertain rewards [9, 10, 11, 12, 13, 14, 15]. These studies have focused on optimising an agent’s expected reward in a single decision, while treating the group’s size and composition as independent variables, unrelated to the decision at hand.…”

The Spread of Beliefs in Partially Modularized Communities

“…Although not denying that beliefs often result from flawed and irrational psychological processes or have been adapted for different information environments than we currently reside (Mann, 2022), our present goal is to explore individual and social processes that are arguably even more fundamental in spreading beliefs and behaviors in a population. In particular, even if people are trying to maximize the utility of their beliefs, rely on unbiased rather than self-serving utility calculations, and do not engage in deceitful messaging, we argue that there will still be pockets of a population having suboptimal beliefs even when most people do not.…”