Distributed networks comprising decision-making units of variable competence are used to perform a sequence of tasks. Estimation of the local competences based solely on comparisons of local decisions on dynamically changing tasks is necessary for improving decision aggregation performance. This paper addresses distributed estimation of local competences on networks of heterogeneous decision-making units. We propose an order-preserving metric that depends on the local network structure to measure the competence of each node in the network instantaneously. We investigate two regimes of operation: First, the tasks are received at low frequency, or sequentially, hence the network can reach a consensus in-between tasks. Second, tasks are received at high frequency, or in batches, in which case, the network reaches to a consensus after tasks are processes locally.