Node certainty in collective decision making

This paper brings into focus the relationship between the location of a decision-making unit in a network of decision makers and its certainty in integrating information toward a decision. A collection of units, each represented by a Drift-Diffusion Model (DDM), accrues evidence in continuous time by observing a (noisy) stimulus. Their task is to make a decision that depends on accurately identifying the stimulus observed. It is shown that common structural centrality measures based on nodal degree or geodesic distance cannot be used to rank the units according to their certainty in integrating information. Instead, the variance associated with the state of a decision-making unit depends on the communication topology in a way that incorporates all possible paths connecting that unit with the rest.