-Or do they? Let's consider grad school admissions rather than the Putnam exam. You want to get into the best school possible, to get access to better mentors and better peers. Getting in to any _particular_ school is a contested rivalrous good (we assume that each can only accept a fixed number of applicants _n_, no matter how good the _n_+1th applicant is on some cosmic absolute scale), but when we consider multiple schools with different admissions standards, there's no dire [dual](http://slatestarcodex.com/2015/07/28/non-dual-awareness/) discontinuity: a small change in application quality results in a small change of best-school-accepted-to (if you don't get into Caltech, go to MIT; if you don't get into MIT; go to Carnegie Mellon; if you ... UC Santa Cruz ... San Diego State ... SF State), much like how a small change in study quality results in a small change in knowledge gained.
+Or do they? Let's consider grad school admissions rather than the Putnam exam. You want to get into the best school possible, to get access to better mentors and better peers. Getting in to any _particular_ school is a contested rivalrous good (we assume that each can only accept a fixed number of applicants _n_, no matter how good the _n_+1th applicant is on some cosmic absolute scale), but when we consider multiple schools with different admissions standards, there's no dire [dual](http://web.archive.org/web/20200423033930/https://slatestarcodex.com/2015/07/28/non-dual-awareness/) discontinuity: a small change in application quality results in a small change of best-school-accepted-to (if you don't get into Caltech, go to MIT; if you don't get into MIT; go to Carnegie Mellon; if you ... UC Santa Cruz ... San Diego State ... SF State), much like how a small change in study quality results in a small change in knowledge gained.