In various real-world scenarios like recommender systems and political surveys, pairwise rankings are commonly collected and utilized for rank aggregation to obtain an overall ranking of items. However, preference rankings can reveal individuals' personal preferences, underscoring the need to protect them before releasing for downstream analysis. In this paper, we address the challenge of preserving privacy while ensuring the utility of rank aggregation based on pairwise rankings generated from the Bradley-Terry-Luce (BTL) model. Using the randomized response mechanism to perturb raw pairwise rankings is a common privacy protection strategy used in practice, but a critical challenge arises because the privatized rankings no longer adhere to the BTL model, resulting in significant bias in downstream rank aggregation tasks. Motivated from this, we propose a debiased randomized response mechanism to protect the raw pairwise rankings, ensuring consistent estimation of true preferences and rankings in downstream rank aggregation. Theoretically, we offer insights into the relationship between overall privacy guarantees and estimation errors from private ranking data, and establish minimax rates for estimation errors. This enables the determination of optimal privacy guarantees that balance consistency in rank aggregation with robust privacy protection. We also investigate convergence rates of expected ranking errors for partial and full ranking recovery, quantifying how privacy protection influences the specification of top-$K$ item sets and complete rankings. Our findings are validated through extensive simulations and a real application.

翻译：在推荐系统与政治调查等现实场景中，成对排名被广泛收集并用于排名聚合以获得项目的整体排序。然而，偏好排名可能泄露个人偏好，因此在发布用于下游分析前需对其进行保护。本文针对基于Bradley-Terry-Luce（BTL）模型生成的成对排名，在保障隐私的同时确保排名聚合效用的挑战展开研究。实践中常用随机响应机制扰动原始成对排名以实现隐私保护，但关键挑战在于经过隐私化处理的排名不再符合BTL模型，导致下游排名聚合任务出现显著偏差。基于此，我们提出一种去偏随机响应机制来保护原始成对排名，确保下游排名聚合中真实偏好与排序的估计一致性。理论上，我们揭示了整体隐私保护与基于私有排名数据估计误差之间的关系，并建立了估计误差的极小极大速率。这使我们能够确定同时平衡排名聚合一致性与鲁棒隐私保护的最优隐私保护水平。我们还研究了部分排名恢复与完全排名恢复的期望排序误差收敛速率，量化了隐私保护对前K项项目集与完整排序规范化的影响。通过广泛模拟实验和实际应用验证了研究结论。