Title: Optimal Evidence Accumulation on Social Networks,
Abstract: A fundamental question in biology is how organisms integrate sensory and
social evidence to make decisions. However, few models describe how both these
streams of information can be combined to optimize choices. Here we develop a
normative model for collective decision making in a network of agents
performing a two-alternative forced choice task. We assume that rational
(Bayesian) agents in this network make private measurements, and observe the
decisions of their neighbors until they accumulate sufficient evidence to make
an irreversible choice. As each agent communicates its decision to those
observing it, the flow of social information is described by a directed graph.
The decision-making process in this setting is intuitive, but can be complex.
We describe when and how the absence of a decision of a neighboring agent
communicates social information, and how an agent must marginalize over all
unobserved decisions. We also show how decision thresholds and network
connectivity affect group evidence accumulation, and describe the dynamics of
decision making in social cliques. Our model provides a bridge between the
abstractions used in the economics literature and the evidence accumulator
models used widely in neuroscience and psychology.