Differentially Private Probabilistic Social Choice in the Shuffle Model

Qingyuan Ding, Keke Sun, Lixin Jiang, Haibo Zhou, Chunlai Zhou

Abstract: Given a profile of ranking lists over a finite set of alternatives, probabilistic social choice seeks to select a probability function over the alternatives on the basis of the pairwise comparison voting data. In this paper, we establish a differentially private formalism for probabilistic social choice in the shuffle model. In the shuffle model, individual voters submit their locally randomized data anonymously through a trusted shuffler which randomly permutes these individual data. Anonymity here plays a double role as a fairness condition and privacy amplification. The crucial step in our construction is to employ spectral clustering to find data-independent cluster centers and then to approximately round each input ranking order to these centers. We proceed to define a local differentially private randomizer plus the shuffler and then implement standard probabilistic social choice protocols such as maximal lottery and random dictatorship. Moreover, we analyze both privacy and utility of the proposed shuffle model and run some experiments to show the effectiveness of our formalism. In the last section, we discuss some related works and future directions.