A new perspective on Kesten's school choice with consent idea

We revisit the school choice problem with consent proposed by Kesten (2010), which seeks to improve the efficiency of the student-optimal deferred acceptance algorithm (DA) by obtaining students’ consent to give up their priorities. We observe that for students to consent, we should use their consent only when their assignments are Pareto unimprovable. Inspired by this perspective, we propose a new algorithm which iteratively reruns DA after removing students who have been matched with underdemanded schools, together with their assignments. While this algorithm is outcome equivalent to Kesten’s EADAM, it is more accessible to practitioners due to its computational simplicity and transparency on consenting incentives. We also ∗We are grateful to the Editor, two anonymous referees, Qian Jiao, Morimitsu Kurino, Ning Sun, Xiang Sun, Chun-Hsien Yeh, and participants at SHUFE Market Design reading group, Academia Sinica, Kyoto KIER, Sun Yat-sen U, HUST, the 5th Shanghai Micro Workshop and CMES for helpful comments. All errors are our own. †Corresponding author. Email addresses: [email protected] (Q. Tang), [email protected] (J. Yu).