Abstract We introduce a modeling framework for stochastic rider‐driver matching in many‐to‐one ridesharing systems, in which drivers have to be selected before the exact rider demand is known. The modeling framework allows for the use of driver booking fees and penalties for unmatched drivers, therefore supporting different system operating modes. We model this problem as a two‐stage stochastic set packing problem. To tackle the intractability of the stochastic problem, we introduce three model approximations and evaluate them on a large set of benchmark instances for three different system operating modes. Our computational experiments show the superiority of some model approximations over others and provide valuable insights on the impact of penalties and booking fees on the system's profitability and user satisfaction.