Social Learning of Ranking: Getting the Top Right despite Local Herding

Abstract

In sequential learning, a group of agents sequentially receives a noisy private signal and observes the predictions of prior agents to estimate a hidden ground truth. While extensively studied for binary signals, we formalize and analyze sequential learning when the hidden ground truth is an ordering of $n$ items, and both private signals and inferences involve pairwise comparisons. A key focus in sequential learning is herding, where agents disregard their private signals to follow the crowd. We show that, while local herding in our model may lead agents to make incorrect pairwise inferences, the global hidden order can still be approximated. Specifically, by aggregating all pairwise comparison outputs, the highest-ranked items can be retrieved. We investigate top-$k$ retrieval across three scenarios: (1) passive aggregation, where information is gathered from the social learning process without intervention; (2) strategic selection, where agents choose their pairwise comparisons dynamically; and (3) aggregation with stubborn nodes, where a very small set of stubborn agents, who base their inferences solely on their private signals, join the mechanism. With query complexity as the number of agents needed for a high-probability estimation, we propose top-$k$ retrieval algorithms with query complexities sublinear in $O(n^2)$, the total number of pairs.