{"id":13280,"date":"2025-03-25T13:01:47","date_gmt":"2025-03-25T20:01:47","guid":{"rendered":"https:\/\/mattfife.com\/?p=13280"},"modified":"2025-01-18T13:13:36","modified_gmt":"2025-01-18T20:13:36","slug":"choosing-something-the-37-rule","status":"publish","type":"post","link":"https:\/\/mattfife.com\/?p=13280","title":{"rendered":"Choosing something: the 37% rule"},"content":{"rendered":"\n

It was the year 1960 and a brainteaser was formulated as \u201cThe Secretary Problem<\/a>\u201d. You need to hire a secretary; there are\u00a0n<\/em>\u00a0applicants to be interviewed. You meet each of them in a random order. You can rank them according to suitability, but once rejected an applicant they cannot be recalled. How can you maximize the probability of picking the best person for the job?\u00a0<\/p>\n\n\n\n

Other versions of this include the \u201cfianc\u00e9 problem\u201d (same idea, but you\u2019re looking for a fianc\u00e9 instead of a secretary) and the \u201cgoogol game\u201d \u2013 in which you are flipping slips of paper to reveal numbers until you decide you\u2019ve probably found the largest of all.<\/p>\n\n\n\n

The answer is\u2026 surprisingly predictable, it turns out.<\/p>\n\n\n\n

\u201cThis basic problem has a remarkably simple solution,\u201d wrote mathematician and statistician Thomas S Ferguson in 1989<\/a>. \u201cFirst, one shows that attention can be restricted to the class of rules that for some integer r<\/em> > 1 rejects the first r<\/em> \u2013 1 applicants, and then chooses the next applicant who is best in the relative ranking of the observed applicants.\u201d<\/p>\n\n\n\n

So, when faced with a stream of random choices and wanting to pick the best, the first thing you do is reject everyone. That is, up to a point. Once you reach that point, just accept the next applicant, suitor, or slip of paper, that beats everything you\u2019ve seen so far.<\/p>\n\n\n\n

The statistics are fascinating; and it says that you reject the first 37% of applicants and then take the next one that’s better than what you’ve seen in the rejected pool. <\/p>\n\n\n\n

This works if it’s apartments, job candidates, or potential life partners.<\/p>\n\n\n\n

Article:<\/p>\n\n\n\n