Binary Mechanisms under Privacy-Preserving Noise

TL;DR

The paper analyzes a binary public-good provision problem under privacy-preserving noise, where agent reports are flipped with probability $\delta$. Using Bayes-Nash IC, IR, and Fourier-analytic tools, it shows that in large economies the asymptotically optimal mechanisms are linear threshold functions, with a quantified tradeoff between privacy (via $\delta$), revenue, and social surplus. The results yield an asymptotic Pareto frontier between noise robustness and revenue, and establish that increasing privacy protection comes at the cost of lower revenue and welfare, with the majority rule serving as a revenue benchmark and tuned-threshold LTFs offering superior noise robustness. The analysis also connects to imperfect knowledge of preferences, showing the same qualitative tradeoffs and threshold structure under alternative interpretations of noise.

Abstract

We study mechanism design for public-good provision under a noisy privacy-preserving transformation of individual agents' reported preferences. The setting is a standard binary model with transfers and quasi-linear utility. Agents report their preferences for the public good, which are randomly ``flipped,'' so that any individual report may be explained away as the outcome of noise. We study the tradeoffs between preserving the public decisions made in the presence of noise (noise sensitivity), pursuing efficiency, and mitigating the effect of noise on revenue.

Figures (2)

• Figure 1: Asymptotic Pareto Frontier
• Figure 2: Revenue and Noise Sensitivity of the Majority Rule

Theorems & Definitions (32)

• Definition 1
• Theorem 1
• Theorem 2
• Remark 1
• Lemma 1: BN-IC
• Proposition 1
• proof
• Proposition 2: Revenue equivalence
• Corollary 1: Maximum expected revenue
• Proposition 3