You have little idea about the talent pool available. You have been told that the market varies wildly from one location to the next and it also varies through time. You placed an ad and have a number of candidates. How do you know which one to hire?
This problem comes up in all kinds of selection scenarios, including looking for a wife/husband or a used vehicle.
There is even an entry in Wikipedia:
...an administrator who wants to hire the best secretary out of rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled...The difficulty is that the decision must be made immediately.
The optimal stopping rule prescribes always rejecting the first applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so farFor small numbers
The optimal thresholds r and probability of selecting the best alternative P for several values of n are shown in the following table.
Finding and checking out vehicles is expensive from a time standpoint. I figure it takes between 90 and 120 minutes to drive to the site, find the vehicle and then go through the checklist Belladonna pulled off the internet.
If it is just Belladonna and I, that is four man-hours. If we want to have the vehicle checked out by a mechanic, then the hours and dollars invested in each candidate goes up.