1
If the pool has one candidate, there is no decision.
You take the candidate. There is no value in waiting because there is no future option.
Optimal stopping, from first principles
Build the problem before naming the rule.
Imagine candidates arriving one at a time. You see only the current candidate, and if you pass, that candidate is gone. The question is: when should you stop searching?
3
Now the picture matters. You can sample one person, use that quality as a rough benchmark, then take the first later candidate who clears it.
The mental primitives
2
If the pool has two candidates, passing is a forced gamble.
You can take the known first candidate, or pass and accept the unknown second candidate. This is where comparison and regret first appear.
3
At three or more candidates, draw the line.
Position becomes the x-axis. Quality becomes the y-axis. Early candidates teach the scale; later candidates are judged against a benchmark.
4
The stopping rule is a threshold.
Stop when the current candidate is good enough that the expected benefit of waiting no longer compensates for the risk of losing them.
A small exercise
This is intentionally rough. The goal is to see direction: more search cost lowers patience; more regret sensitivity raises the bar.
Sample first 37 candidates.
The whole idea in one inequality
stop if current value >= expected value of waiting - search cost