Optimal Stopping

We were trying to sell an old car recently and had placed it in a used car parking lot. These lots charge a monthly rent. So, you are incentivized to sell your vehicle within the first month. The question for us, then, – when is the optimal time to sell? For example, do we hold out till the end of the month and wait for the best offer?

Luckily, mathematics has a solution for us. The optimal time to stop is at 37%. If you have a 100 candidates for your next role, the most optimal way to make a decision on the best candidate is to reject the first 37 and then pick the first of the next few that is better than the first 37. Essentially, the algorithm suggests we use the first 37 to calibrate.

Optimal stopping can be extended to time as well. In this case, we had 30 days to sell and 37% of 30 days is 11.1 days. By that logic, we would hold out for the first 11 days and then sell – assuming a half decent offer comes along. Our first offer came after 14 days and we sold for a price that was eventually slightly lesser than we’d planned for. But, we had no regrets because math told us that we’d made the optimal decision.

Algorithms like optimal stopping are likely the future of psychology and behavioral economics. Optimal stopping can be applied to choosing a restaurant, a spouse, and while buying a house. As we learn about our fallibility in making decisions, we can use algorithms like this one to get better at making decisions.

(H/T: Algorithms to Live By – Brian Christian and Tom Griffiths)