In data ranking applications, pairwise annotation is often more consistent than cardinal annotation for learning ranking models. We examine this in a case study on ranking text passages for argument convincingness. Our task is to choose text passages that provide the highest-quality, most-convincing arguments for opposing sides of a topic. Using data from a deployed system within the Bing search engine, we construct a pairwise-labeled dataset for argument convincingness that is substantially more comprehensive in topical coverage compared to existing public resources. We detail the process of extracting topical passages for queries submitted to a search engine, creating annotated sets of passages aligned to different stances on a topic, and assessing argument convincingness of passages using pairwise annotation. Using a state-of-the-art convincingness model, we evaluate several methods for using pairwise-annotated data examples to train models for ranking passages. Our results show pairwise training outperforms training that regresses to a target score for each passage. Our results also show a simple ‘win-rate’ score is a better regression target than the previously proposed page-rank target. Lastly, addressing the need to filter noisy crowd-sourced annotations when constructing a dataset, we show that filtering for transitivity within pairwise annotations is more effective than filtering based on annotation confidence measures for individual examples.