When every rejection is irreversible, choosing well begins with knowing when not to choose. An initial sample can become the standard used for every later decision.
The optimal choice
Riddle statement
You will interview a known number \(N\) of candidates for a job. They arrive one at a time in a uniformly random order, and you can rank them without ties.
After each interview, you must decide immediately: hire that candidate and stop, or reject them permanently. If you reach the final candidate without hiring anyone, you must hire that candidate.
You want to maximize the probability of selecting the best candidate overall.
What is the optimal strategy, and what success probability does it achieve?