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I write data mining software professionally, and one weakness that comes to mind is the deduplication process. In order to combine data from different sources, the software has to determine which entries correspond to the same person. It does this by looking for common elements with a low false positive rate. If two records have the same phone number, email address, site plus account name, social security number, or name-address pair, they are almost certainly the same person, so they will be combined. This relation is transitive, so if A has the same phone number as B and B has the same email address as C, then A, B, and C will all be assumed to be the same person.
You can subvert this by creating records which map as equivalent to two different people, such as by having one person's phone number and another person's email address. If a data source contains too many entries like this, it's useless unless there's an easy way to filter them out. If a data source contains just a few entries like this, data miners are likely to get confused. Note that this is not necessarily a good idea, since having a computerized bureaucracy be confused about your identity can have very inconvenient consequences. It is also possible to detect and defeat this strategy, by looking for deduplications with strange results, but this is tricky in practice, since people often really do have multiple names (maiden names, alternate spellings), phone numbers, email addresses etc.