  A sequence of social sensors estimate an unknown parameter (modeled as a
state of nature) by performing Bayesian Social Learning, and myopically
optimize individual reward functions. The decisions of the social sensors
contain quantized information about the underlying state. How should a fusion
center dynamically incentivize the social sensors for acquiring information
about the underlying state? This paper presents five results. First, sufficient
conditions on the model parameters are provided under which the optimal policy
for the fusion center has a threshold structure. The optimal policy is
determined in closed form, and is such that it switches between two exactly
specified incentive policies at the threshold. Second, it is shown that the
optimal incentive sequence is a sub-martingale, i.e, the optimal incentives
increase on average over time. Third, it is shown that it is possible for the
fusion center to learn the true state asymptotically by employing a sub-optimal
policy; in other words, controlled information fusion with social sensors can
be consistent. Fourth, uniform bounds on the average additional cost incurred
by the fusion center for employing a sub-optimal policy are provided. This
characterizes the trade-off between the cost of information acquisition and
consistency for the fusion center. Finally, when it is sufficient to estimate
the state with a degree of confidence, uniform bounds on the budget saved by
employing policies that guarantee state estimation in finite time are provided.
