In this paper, we propose a risk-based coordination method for the Multi-Robot Task Allocation (MRTA) problem in human-populated environments. We introduce risk-based bids that incorporate human trajectory prediction uncertainties and furthermore, social costs in their formulation. We demonstrate the effectiveness of including a predictive component in the risk formulation despite the lack of accurate position estimation for humans through an extensive suite of experiments. This is done by means of testing different levels of prediction error for known human trajectories and in a separate approach, using a Kalman filter for human trajectory estimation. Furthermore, we propose different risk formulations and evaluate their performance in a high-fidelity simulator. Additionally, a comparative study targeting human-agnostic planning at both navigation and planning levels, human-aware navigation and planning based on deterministic costs, and risk-based human-aware planning with no individual human-aware navigation has been conducted. Results confirm that risk-based bids lead to more socially acceptable team plans that reduce the need for the lower level individual human-aware navigation to be activated. Risk-based plans that account for social costs, prevent difficult social situations that can lead to less effective human-aware navigation, such as traversing narrow passages occupied by humans.