# Privacy-Preserving Monotonicity of Differential Privacy Mechanisms
## 2 Related Works
With additional knowledge such as the variation in the resemblance due to different perturbed locations, a user could be in better control of balancing location privacy and service accuracy. In response to users' natural personalized privacy requirements for privacy spatial data aggregation problem of the local setting, a novel personalized local differential privacy model provided a better trade-off between location privacy and utility [61]. The model could achieve desirable utility and provide rigorous privacy-preserving. However, location privacy-preserving based on differential privacy does not provide the measurement method to measure the trade-off. Thus, the definition of privacy-preserving monotonicity is imperative to measure the trade-off. Differential privacy achieves the trade-off in recommendation service. [PERSON] and [PERSON] [62] found that several leading approaches in the Netflix Prize competition could be adapted to provide differential privacy without significantly degrading their accuracy. Although the loss in accuracy decreased as more data became available for a fixed value of the privacy parameter, these approaches did not immediately admit applying to privacy-preserving computations of latent factors and incorporation in differential privacy framework of advanced methods for collaborative filtering. [PERSON] et al. [27] proposed a mechanism to achieve differential privacy graph-link analysis-based social recommendation. The proposed mechanism achieved a better trade-off between privacy and accuracy in comparison with existing work. However, recommendation service with differential privacy does not provide an approach to measure the trade-off. Thus, this problem is covered the proposed definition of privacy-preserving monotonicity. In further application fields, differential privacy can also ensure the trade-off. [PERSON] et al. [28] adopted differential privacy aggregates of web browsing behavior that could be released in real time while preserving the utility of shared data. Although the quality of the privacy of releasing data by this solution closely resembled that of the unperturbed aggregates, the scalability of multivariatemethod of this solution became an immediate challenge when the domain of web pages was large. [PERSON] et al. [29] proposed an efficient distortion-based privacy-preserving metering scheme that protected an individual customer's privacy and provided the complete power consumption distribution curve of a multitude of customers without privacy invasion. This scheme provided a proper trade-off between privacy-preserving and accuracy of power consumption distribution reconstruction in smart grids. [PERSON] et al. [30] proposed a novel framework that allowed the spectrum-sensing provider to select mobile users for executing spatiotemporal spectrum-sensing tasks without violating the location privacy of mobile users. This framework could provide differential location privacy to mobile users while ensuring that the spectrum-sensing provider could accomplish spectrum-sensing tasks with overwhelming probability and the minimum cost. [PERSON] and [PERSON] [31] showed that the exponential mechanism could be implemented as a truthful mechanism while still preserving differential privacy for any mechanism design problem with the objective of maximizing social welfare. The trade-off between privacy and social welfare was asymptotically optimal in combinatorial public project problem and multiple items auction. However, these application fields with differential privacy do not show any method to measure the trade-off. Thus, the purpose of the definition of privacy-preserving monotonicity measures the trade-off. To sum up, currently works only achieve the trade-off between privacy and utility in differential privacy and its applications. However, there is no unified measurement of the trade-off between privacy and utility in differential privacy as we know.