Category: Decision Making

Optimal Stopping

Leave a comment

San Francisco is a hot rental market.  Most apartments are snatched up within a few days of being listed.  Imagine you are moving to San Francisco and want to find the ideal apartment.  You only have one opportunity to view each apartment and must decide on the spot if you want it.  If you reject it the apartment will be taken by the next renter.  How long should you spend on the apartment search in order to feel confident that you have found the ideal spot?  This is an example of the optimal stopping problem.

algorithmsAccording to the book Algorithms to Live By, “the crucial dilemma is not which option to pick, but how many options to even consider.”  The San Francisco situation is an example from the book which demonstrates that a person must gather enough information to become familiar with the market before selecting.  Pick too early and you risk taking a lousy apartment when the next one would have been superior.  Pick too late and you will regret all the great apartments you passed on. Is there an ideal solution to this dilemma?

Yes! According to the authors it is 37%!  This means you should spend 37% of your allotted time or the first 37% of the potential selections just looking.  This will calibrate you to the market.  After that point, take the first option which exceeds everything else you have looked at so far.  For example, if you have only one month to find an apartment, spend the first eleven days just looking.  On day twelve be ready to commit to the next apartment that is better than all the other ones you viewed up to that point.  This is claimed to be a mathematically provable optimum solution.

To learn more about optimal stopping, pick up a copy of Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian and Tom Griffiths.

Explore / Exploit

Leave a comment

Quick question: when it is time to select a spot for a special dinner would you rather return to an old favorite restaurant or take a chance on a new place that no one has been to before?  This choice is an example of a classic decision making challenge known as the Explore / Exploit trade off.

algorithmsIn order to discover new and exciting things in life, we have to be willing to explore options.  This will naturally result in some failures, but the treasures out there waiting to be discovered can be worth the effort.  However, once we have found a great resource it is tempting to keeping going back to the well to get as much of it as possible.  In the book, Algorithms to Live By, the authors sum up the trade off in this way: “Exploration is gathering information, and exploitation is using the information you have to get a known good result.”

In general, the research shows that at the beginning of a given time frame it is much better to focus energy on exploring.  After the halfway point it makes more sense to exploit the good stuff you have found.  I recently used this logic with my daughter on a trip to the Legoland theme park.  I encouraged her to try out as many new rides as possible on the first day of our visit, and then use the second day to go back to the rides she enjoyed the most and do them as often as she could.  It made for a very enjoyable experience as she braved new exciting roller coaster experiences, but still had time for her old calmer favorites.

So don’t be shy, go out and explore!  However, plan to enjoy the fruits of that exploration by saving time to exploit your favorites.