Fitness technologies such as wearables and sit-stand desks are increasingly being used to fight sedentary lifestyles by encouraging physical activity. However, adherence to such technologies decreases over time because of apathy and increased dismissal of behavioral nudges. To address this problem, we introduced shared autonomy in the context of sit-stand desks, where user input is integrated with robot autonomy to control the desk and reduce sedentary behavior and investigated user reactions and preferences for levels of automation with a sit-stand desk. As demographics affect user acceptance of robotic technology, we also studied how perceptions of nonvolitional behavior change differ across cultures (United States and India), sex, familiarity, dispositional factors, and health priming messages. We conducted a web-based vignette study in the United States and India where a total of 279 participants watched video vignettes of a person interacting with sit-stand desks of various levels of automation and answered questions about their perceptions of the desks such as ranking of the different levels of automation. Participants generally preferred either manual or semiautonomous desks over the fully autonomous option (P<.001). However, participants in India were generally more amenable to the idea of nonvolitional interventions from the desk than participants in the United States (P<.001). Male participants had a stronger desire for having control over the desk than female participants (P=.01). Participants who were more familiar with sit-stand desks were more likely to adopt autonomous sit-stand desks (P=.001). No effects of health priming messages were observed. We estimated the projected health outcome by combining ranking data and hazard ratios from previous work and found that the semiautonomous desk led to the highest projected health outcome. These results suggest that the shared autonomy desk is the optimal level of automation in terms of both user preferences and estimated projected health outcomes. Demographics such as culture and sex had significant effects on how receptive users were to autonomous intervention. As familiarity improves the likelihood of adoption, we propose a gradual behavior change intervention to increase acceptance and adherence, especially for populations with a high desire for control.