The rise of big data technologies, allowing firms to collect detailed consumer data to estimate their willingness to pay, has reignited the longstanding debate on the welfare implications of price discrimination. A significant difficulty in regulating data collection practices is that it is close to impossible to perfectly monitor and control how firms use consumer data, which makes highly targeted regulation impractical. Often the relevant question is if data collection should be permitted, without knowing how much information the firm already has nor how much additional information it might be able to collect.