Worst-Case Privacy
Mr Tianhao Liu
Ph.D. Candidate in Economics
Columbia University
How should privacy loss be assessed? Motivated by current privacy discourse, I formalize the principle of uniform protection: if an information structure violates a privacy standard, it should also be deemed unacceptable even when used infrequently. Together with a standard (Blackwell) monotonicity requirement, uniform protection defines the class of Worst-Case Privacy measures. I show that any such measure can be decomposed into the losses of individual signals and aggregated through their maximum. When the privacy threats are predictions of protected attributes, the loss of a signal depends on how much it distinguishes between each pair of attributes, measured by log-likelihood ratios. I apply these measures to canonical economic settings. In matching markets, a sharp tradeoff arises: as stable mechanisms shift from firmoptimal to worker-optimal, workers’ welfare improves but their privacy deteriorates. In a voting application, the optimal privacy-constrained rule exhibits choice reversal when a candidate’s vote count is extreme.














