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The development of Internet technology enables an analysis on the wholepopulation rather than a certain number of samples, and leads to increasingrequirement for privacy protection. Local differential privacy (LDP) is aneffective standard of privacy measurement; however, its large variance of meanestimation causes challenges in application. To address this problem, thispaper presents a new LDP approach, an improved Christofides mechanism.  It compared four statistical survey methods for conducting surveys onsensitive topics -- modified Warner, Simmons, Christofides, and the improvedChristofides mechanism. Specifically, Warner, Simmons and Christofidesmechanisms have been modified to draw a sample from the population withoutreplacement, to decrease variance. Furthermore, by drawing cards withoutreplacement based on modified Christofides mechanism, we introduce a newmechanism called the improved Christofides mechanism, which is found to havethe smallest variance under certain assumption when using LDP as a measurementof privacy leakage. The assumption is do satisfied usually in the real world.Actually, we decrease the variance to 28.7% of modified Christofidesmechanism's variance in our experiment based on the HCOVANY dataset -- a realworld dataset of IPUMS USA. This means our method gets a more accurate estimateby using LDP as a measurement of privacy leakage. This is the first time theimproved Christofides mechanism is proposed for LDP framework based oncomparative analysis of four mechanisms using LDP as the same measurement ofprivacy leakage.

An Improved Christofides Mechanism for Local Differential Privacy Framework