  As machine learning (ML) is deployed by many competing service providers, the
underlying ML predictors also compete against each other, and it is
increasingly important to understand the impacts and biases from such
competition. In this paper, we study what happens when the competing predictors
can acquire additional labeled data to improve their prediction quality. We
introduce a new environment that allows ML predictors to use active learning
algorithms to purchase labeled data within their budgets while competing
against each other to attract users. Our environment models a critical aspect
of data acquisition in competing systems which has not been well-studied
before. We found that the overall performance of an ML predictor improves when
predictors can purchase additional labeled data. Surprisingly, however, the
quality that users experience -- i.e. the accuracy of the predictor selected by
each user -- can decrease even as the individual predictors get better. We show
that this phenomenon naturally arises due to a trade-off whereby competition
pushes each predictor to specialize in a subset of the population while data
purchase has the effect of making predictors more uniform. We support our
findings with both experiments and theories.
