Binary Decisions of Large Cliques of Evidence Accumulators

We consider cliques of N evidence accumulators making a binary decision based on noisy observations. Each agent's evidence is a drift-diffusion process on a symmetric, bounded domain with absorbing boundaries. An agent makes an immutable decision when their evidence reaches one of the boundaries (thresholds). Prior to a decision, each agent's evidence is an independent stochastic process. Following a decision, each agent's evidence receives a bump equal to the value of the threshold corresponding to the decision. In large cliques, such a decision can induce a large fraction of the agents to agree with the initial decider. If the first decider is correct, this bodes well for the overall performance of the clique. However, if the initial decider is incorrect, the overall performance of the clique can be disastrous. We derive asymptotic results conveying what fraction of agents agree with the initial decider upon observing their decision and how the remaining agents decide therafter to agree with the initial decider or collectively disagree with them. We also show how the framework of the evidence accumulation in cliques can be modified so that it is self-correcting and, even if the first decision is wrong, have the majority of the clique choose the correct decision.