Symmetric-ISA (instruction set architecture) asymmetric-performance multicore processors (AMPs) were shown to deliver higher performance per watt and area than symmetric CMPs (Chip Multi-Processors). Previous work has shown that this potential of AMP systems can be realizable thanks to the OS scheduler. Existing scheduling schemes that deliver fairness and priority enforcement on AMPs do not cater to the fact that applications in a multiprogram workload may derive different benefit from using fast cores in the system. As a result, they are likely to perform thread-to-core mappings that degrade the system throughput. To address this limitation, we propose Prop-SP, a scheduling algorithm that aims to improve the throughput-fairness trade-off on AMPs. Our evaluation on real hardware, and using scheduler implementations on a general-purpose OS, reveals that Prop-SP delivers a better throughput-fairness trade-off than state-of-the-art schedulers for a wide variety of multi-application workloads.