“…The propensity score theorem says that for research designs in which treatment status, D i , is independent of potential outcomes conditional on covariates, X i , treatment status is also independent of potential outcomes conditional on the propensity score, that is, conditional on E[D i |X i ]. In work building onAbdulkadiroglu et al (2017a), the DA propensity score has been used to study schools(Bergman, 2018), management training(Abebe et al, 2019), and entrepreneurship training (Pérez Vincent and Ubfal, 2019).2 Non-lottery tie-breaking embedded in centralized assignment schemes has been used in econometric research on schools in Chile(Hastings et al, 2013; Zimmerman, 2019), Ghana(Ajayi, 2014), Italy(Fort et al, 2020), Kenya(Lucas and Mbiti, 2014), Norway(Kirkeboen et al, 2016), Romania (Pop-Eleches and Urquiola, 2013), Trinidad and Tobago(Jackson, 2010(Jackson, , 2012Beuermann et al, 2016), and the U.S (Abdulkadiroglu et al, 2014;Dobbie and Fryer, 2014;Barrow et al, 2016)…”