Democratic AI, aiming at developing AI systems aligned with human values, holds promise for making AI services accessible to people. However, concerns have been raised regarding the participation of non-technical individuals, potentially undermining the carefully designed values of AI systems by experts. In this paper, we investigate Democratic AI, define it mathematically, and propose a user-centric evolutionary democratic AI (u-DemAI) framework. This framework maximizes the social values of cloud-based AI services by incorporating user feedback and emulating human behavior in a community via a user-in-the-loop iteration. We apply our framework to a medical AI service for brain age estimation and demonstrate that non-expert users can consistently contribute to improving AI systems through a natural democratic process. The u-DemAI framework presents a mathematical interpretation of Democracy for AI, conceptualizing it as a natural computing process. Our experiments successfully show that involving non-tech individuals can help improve performance and simultaneously mitigate bias in AI models developed by AI experts, showcasing the potential for Democratic AI to benefit end users and regain control over AI services that shape various aspects of our lives, including our health.