Balance tests as a learning problem

This paper builds on information from different administrative sources to construct a dataset of over 3,000 lotteries to distribute houses to low-income citizens. It proposes using machine learning methods to test balance on the pre-treatment covariates. If the lotteries are believable we should see no predictive power of the pre-treatment covariates on the treatment assingment.  We would like to see a perfect 45-degree line - meaning that the Random Forest was unable to predict any of the lotteries.