In the first stage of a re-ranking pipeline, an inexpensive ranking model is typically deployed to retrieve a set of documents that are highly likely to be relevant to the user's query. The retrieved documents are then re-ranked by a more effective but expensive ranking model, e.g., a deep neural ranker such as BERT. However, in such a standard pipeline, no new documents are typically discovered after the first stage retrieval. Hence, the amount of exposure that a particular group of documents - e.g., documents from a particular demographic category - can receive is limited by the number of documents that are retrieved in the first stage retrieval. Indeed, if too few documents from a group are retrieved in the first stage retrieval, ensuring that the group receives a fair amount of exposure to the user may become infeasible. Therefore, it is useful to identify more documents from underrepresented groups that are potentially relevant to the query during the re-ranking stage. In this work, we investigate how deploying adaptive re-ranking, which enables the discovery of additional potentially relevant documents in the re-ranking stage, can improve the exposure that a given group of documents receives in the final ranking. We propose six adaptive re-ranking policies that can discover documents from underrepresented groups to increase the disadvantaged groups' exposure in the final ranking. Our experiments on the TREC 2021 and 2022 Fair Ranking Track test collections show that our policies consistently improve the fairness of the exposure distribution in the final ranking, compared to standard adaptive re-ranking approaches, resulting in increases of up to ~13% in Attention Weighted Ranked Fairness (AWRF). Moreover, our best performing policy, Policy 6, consistently maintains and frequently increases the utility of the search results in terms of nDCG.

Multilingual information retrieval (MLIR) considers the problem of ranking documents in several languages for a query expressed in a language that may differ from any of those languages. Recent work has observed that approaches such as combining ranked lists representing a single document language each or using multilingual pretrained language models demonstrate a preference for one language over others. This results in systematic unfair treatment of documents in different languages. This work proposes a language fairness metric to evaluate whether documents across different languages are fairly ranked through statistical equivalence testing using the Kruskal-Wallis test. In contrast to most prior work in group fairness, we do not consider any language to be an unprotected group. Thus our proposed measure, PEER (Probability of Equal Expected Rank), is the first fairness metric specifically designed to capture the language fairness of MLIR systems. We demonstrate the behavior of PEER on artificial ranked lists. We also evaluate real MLIR systems on two publicly available benchmarks and show that the PEER scores align with prior analytical findings on MLIR fairness. Our implementation is compatible with ir-measures and is available at http://github.com/hltcoe/peer_measure.