Realistic college application advice, by Ali and Shorrer in the AER

 Here's a nice paper modeling the advice that high school guidance counselors traditionally give about college applications, reflecting the fact that colleges' admissions decisions are correlated, and applications are often limited. 

Hedging When Applying: Simultaneous Search with Correlation by S. Nageeb Ali and Ran I. Shorrer, American Economic Review (Forthcoming)

Abstract: Applicants to schools, colleges, and jobs hedge by applying to a broad range of options, including reaches, matches, and safeties. We develop a simultaneous-search framework that rationalizes this practice. In this framework, the admissions process is correlated across schools so that if an applicant is rejected by one school, she is more likely to be rejected by more selective schools. We find that an applicant then optimally targets both safeties and reaches. We characterize how the optimal portfolio varies with the applicant’s beliefs, risk attitudes, and application costs, and offer an algorithm that delivers the optimal portfolio in polynomial time.

And here are the opening paragraphs:

"An applicant to schools, colleges, or jobs typically does not know if or where her applications would be accepted. To hedge her bets, she might target some places she deems safeties, others she views to be matches for her qualifications, and some that are reaches. Hedging is common; indeed, this strategy is generally recommended to college applicants by guidance counselors and advisers.

'Why hedge? Intuitively, an applicant might see admissions decisions as being correlated across schools. For instance, in US college and graduate admissions, an applicant might not know where she stands in the pool, what her letters of recommendation say, or how schools assess her essay. An applicant’s prospects are correlated also in centralized admissions protocols in which the applicant has to first specify a portfolio of schools and then take a single exam that determines where she is admitted. Such protocols have featured in China, Ghana, Kenya, Mexico, Turkey, and the UK. Finally, “single tie-breaking” matching procedures, in which a single lottery is used to allocate overdemanded seats, necessarily also correlates admissions decisions. In all these cases, if one school rejects an applicant, then it is more likely that other schools would also do so. This force might impel her to apply broadly."