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Optimal decision making in social networks

Banff International Research Station for Mathematical Innovation and Discovery

Humans and other animals integrate information across modalities and across time to perform simple tasks nearly optimally. However, it is unclear whether humans can optimally integrate information in the presence of redundancies. For instance, different modalities, or different agents in a social network can transmit information received from the same or related sources. What computations need to be performed to combine all incoming information while taking into account such redundancies? Moreover, if information propagates through a larger network, does locally optimal inference at each node permit optimal inference of all available information downstream? To address these questions we study a simple Bayesian network model for optimal inference. We first investigate feedforward networks where nodes (agents) in the first layer estimate a single parameter drawn from a Gaussian distribution. The agents pass their beliefs about these estimates on to nodes in the next layer where they are optimally integrated, accounting for redundancies. The information is then propagated analogously across other layers until it reaches a final observer. We give a simple criterion for when the final estimate is nonoptimal, showing that redundancies can significantly impact performance even when information is integrated locally optimally by every agent. This gives us a benchmark to compare to the case when observers do not account for such correlations. We also show that when connections between layers are random, the probability that the final observer can perform optimal inference approaches 1 if intervening layers contain more nodes than the first. We also examine other factors in the network structure that lead to globally suboptimal inference, and show how the process compares to the case of parameters that follow non-Gaussian distributions, and how information propagates through recurrent networks. This work has the potential to account for how optimal individual performance can be detrimental for group intelligence.

Mathematics; Biology and other natural sciences; Probability theory and stochastic processes; Mathematical biology

video/mp4

Author affiliation: University of Houston

2016-06-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58252

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/