The Algorithm Advantage: Ranked Application Systems Outperform Decentralized and Common Applications in Boston and Beyond

School choice systems increasingly use common applications, where students can apply to multiple schools on a single form, though schools make admission decisions independently. We model three application systems: a common application, a decentralized system with costly separate applications, and a ranked-choice system using a matching algorithm. Our model shows that while a common application may expand access, it increases competition and may produce worse matches than a decentralized system where application costs encourage more selective applications. Ranked-choice systems combine reduced application costs with preference-based matching that reduce mismatches. We examine these predictions by analyzing how Boston's charter school sector was affected when it adopted an online common application. Counterfactual simulations suggest the common application performs no better than alternatives on several metrics and did little to increase access for disadvantaged groups. A ranked system consistently outperforms a common application across various levels of competition and assumptions on preference stability between application and enrollment stages.