I don't think you can make that conclusion. I think you're making the assumption that all three data points are needed for all 87%. But obviously some people c

I don't think you can make that conclusion. I think you're making the assumption that all three data points are needed for all 87%. But obviously some people can be uniquely identified based on just {zip, date or birth}, such that gender isn't necessary. So the distribution could e.g. be 8% same, 8% opposite, 5% both, 79% neither, and explain the original numbers without triggering the paradox.