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In any situation where a set of personal attributes are revealed, there is a chance that revealed data can be linked back to its owner. Examples of such situations are publishing user profile micro-data or information about social ties, sharing profile information on social networking sites, or revealing personal information in computer-mediated communication (CMC). Measuring user anonymity is the first step to ensuring that the identity of the owner of revealed information cannot be inferred. Most current measures of anonymity ignore important factors such as the probabilistic nature of identity inference, the inferrer's outside knowledge, and the correlation between user attributes. Furthermore, in the social computing domain, variations in personal information and various levels of information exchange among users make the problem more complicated. We present an information-entropy-based realistic estimation of the user anonymity level to deal with these issues in social computing in an effort to help predict the identity inference risks. We then address implementation issues of online protection by proposing complexity reduction methods that take advantage of basic information entropy properties. Our analysis and delay estimation based on experimental data show that our methods are viable, effective, and efficient in facilitating privacy in social computing and synchronous CMCs.