As algorithms powered by Artificial Intelligence (AI) are increasingly involved in the management of organizations, it becomes imperative to conduct human-centered AI management research and understand people's feelings and behaviors when machines gain power over humans. The two mainstream methods - vignette studies and case studies - reveal important but inconsistent insights. Here we discuss the respective limitations of vignette studies (affective forecasting errors, biased media coverage, and question substitution) and case studies (social desirability biases and lack of random assignment and control conditions), which may lead them to overrate negative and positive reactions to AI management, respectively. We further discuss the advantages of a third method for mitigating these limitations: field experiments on crowdsourced marketplaces. A proof-of- concept study on Amazon Mechanical Turk (Mturk; as a world-leading crowdsourcing platform) showed unique human reactions to AI management, which were not perfectly aligned with those in vignette or case studies. Participants (N N = 504) did not differ significantly under AI versus human management, in terms of performance, intrinsic motivation, fairness perception, and commitment. We suggest that crowdsourced marketplaces can go beyond human research subject pools and become models of AI-managed workplaces, facilitating timely behavioral research and robust predictions on human-centered work designs and organizations.