This paper proposes a novel algorithmic market mechanism to address key challenges in individual data markets. Current data collection practices lack transparency and proper compensation, leading privacy-conscious users to opt out and creating biased data sets. Our proposed mechanism enables an intermediary platform to obtain unbiased samples of individual-level data while appropriately compensating users for privacy loss. Through theoretical analysis and simulations using both synthetic and real-world data sets, the authors demonstrate that their mechanism provides unbiased data samples at near-optimal cost compared with benchmark approaches. The mechanism outperforms both fixed-compensation methods and centralized-optimization approaches, even when platforms have partial information about user privacy preferences. Surprisingly, platforms achieve better outcomes by using this market mechanism rather than relying on estimated privacy preferences from user behavior. The approach is practical to implement, using straightforward sampling and conventional compensation mechanisms rather than complex techniques, like differential privacy. The mechanism enables creation of effective data markets that benefit both data subjects and buyers while ensuring compliance with regulations requiring transparency and consent. The findings are particularly relevant as new privacy regulations emerge globally and third-party tracking faces increased constraints, providing a viable solution for improving data quality and fairness in digital markets.