A stopping rule is used to determine when one should stop searching for things like a spouse, parking spaces, investment deals, a new home, a new secretary, etc.... The "look then leap" stopping rule suggest that we should just look for awhile so that we increase the likelihood of encountering the optimal spouse, the optimal parking spot, the optimal investment deal, the optimal house, the optimal secretary, etc... The question is how long we should keep looking before deciding to leap?

A considerable amount of research has been done to find an optimal strategy for determining when we should stop looking. It turns out that we should stop looking at secretary applicants after we have interviewed 37% percent of them. After that we should jump at the next secretary that is better than the previous secretaries we interviewed. If we are looking for a marriage partner, then we should figure out how long we are prepared to look for that partner and once we have used up 37% of that time, we should consider proposing to the next marriage partner that we regard as better than the ones we have been with to date. The 37% rule applies to either the number of items to be searched or the amount of time we have to search.

If you use this optimal strategy then 37% of the time you will pick the optimal item you are looking for. There is no optimal stopping rule that gives you certainty that you will pick the optimal item. The best investment deal may have been in the 37% of deals you reviewed to date and didn't make an offer on or perhaps if you waited until you reviewed 60% of the deals you would have found the optimal deal. If you set your optimal stopping rule at some number other than 37%, however, your chance of finding the optimal item will be less than 37%. That is all that optimal means in this context.

This form of the optimal stopping rule makes alot of assumptions so whether it is applicable or not depends on your particular situation. For example, if you are allowed to go back and pick the best secretary of the 37% you have interviewed, or if the secretary is allowed to refuse your offer, then the math behind the stopping rule changes and we would have a different optimal strategy for that situation.

The "look then leap" stopping rule also assumes that we are ranking items relative to each other (ordinal scale) rather than relative to some absolute scale (cardinal ranking). If we have some absolute criteria we can use to evaluate candidates then we can pick a candidate if they exceed some threshold we have set for selecting them. Using a "threshold rule" to determine when to stop is another stopping rule stategy we can use.

A "threshold rule" allows us to potentially finish our search faster than using the "look then leap" strategy. Instead of looking for who you might "love" the most by comparing each to the last, you instead set some criteria that your potential marriage partner must meet and as soon as the person meets those criteria you propose.

Stopping rules are important to determining when we should walk away from an investment. Those who lost everything during the 1929 Wall Street crash did not stop in time. Gerald Loeb pulled out before the crash and credited his stopping rule for his success in doing so: "If an investment loses 10 percent of its initial value, sell it".

There is also a rule when climbing Mount Everest that if you are not on the top by 2 o'clock then you should turn around. It does not end well for those who ignore this rule.

In my next blog on The Lean Startup book, I'll be dealing with the chapter titled Pivot and we'll see that this is very much concerned with knowing when to stop in your present course and when to persevere.

Stopping rules can be informed by mathematics and probability theory but can also involve general rules of thumb that have proved useful in the past. This discussion of stopping rules was inspired by Algorithms to Live By: The Computer Science of Human Decisions (2016) which focused on the more formal approaches to stopping rules, and Simple Rules: How to Thrive in a Complex World (2015) which focused on the rules of thumb that are used to guide our stopping decisions.