For downlink multi-user non-orthogonal multiple access (NOMA) systems with successive interference cancellation (SIC) receivers, and a base-station not possessing the instantaneous channel gains, the fundamental relationship between the target rates and power allocation is investigated. It is proven that the total interference from signals not removed by SIC has a fundamental upper-limit which is a function of the target rates, and the outage probability is one when exceeding this limit. The concept of well-behaved power allocation strategies is defined, and its properties are proven to be derived solely based on the target rates. The existence of power allocation strategies that enable NOMA to outperform OMA in per-user outage probability is proven, and are always well-behaved for the case when the outage probability performance of NOMA and OMA are equal for all users. The proposed SIC decoding order is then shown to the most energy efficient. The derivation of well-behaved power allocation strategies that have improved outage probability performance over OMA for each user is outlined. Simulations validate the theoretical results, demonstrating that NOMA systems can always outperform OMA systems in outage probability performance, without relying on the exact channel gains.