I had the pleasure of serving on Honorata Mazepus' dissertation committee and receiving the answer to this question first-hand. In her dissertation, Honorata investigated which factors contribute to perceptions of political authorities as legitimate by individuals socialized in different political regimes. She found that citizens care about the outcomes they derive from governing (e.g., material welfare and stability), but are even more so are concerned with the fairness in which goods and services are distributed across society. Results were surprisingly consistent across regimes, thus challenging the notion that there may be something unique about the expectations about political authorities that citizens in non-democratic regimes have.
Honorata did a fabulous job at her defense and very deservedly goes by Dr. Mazepus now!