### Solving hard decisions

Deciding when to stop your quest for the ideal apartment, or ideal spouse, depends entirely on how long you expect to be looking, says Brian Christian. The first one you check will be the best you’ve seen, but it’s unlikely to be the best you’ll ever see. So you keep looking and keep finding new bests, though ever less frequently, and you start to wonder if maybe you refused the very best you’ll ever find. And the search is wearing you down. When should you take the leap and look no further?

The answer from computer science is precise: 37% of the way through your search period. If you’re spending a month looking for an apartment, you should calibrate (and be sorely tempted) for 11 days, and then you should grab the next best-of-all you find. Likewise with the search for a mate. If you’re looking from, say, age 18 to 40, the time to shift from browsing and having fun to getting serious and proposing is at age 26.1. (However, if you’re getting lots of refusals, “propose early and often” from age 23.5. Or, if you can always go back to an earlier prospect, you could carry on exploring to age 34.4.)

This “Optimal Stopping” is one of twelve subjects examined in Christian’s (and co-author Tom Griffiths’) book, _Algorithms to Live By_. (The other subjects are: Explore/Exploit; Sorting; Caching; Scheduling; Bayes’ Rule; Overfitting; Relaxation; Randomness; Networking; Game Theory; and Computational Kindness. An instance of Bayes’ Rule, called the Copernican Principle, lets you predict how long something of unknown lifespan will last into the future by assuming you’re looking at the middle of its duration—hence the USA, now 241 years old, might be expected to last through 2257.)

Christian went into detail on the Explore/Exploit problem. Optimism minimizes regret. You’ve found some restaurants you really like. How often should you exploit that knowledge for a guaranteed good meal, and how often should you optimistically take a chance and explore new places to eat? The answer, again, depends partly on the interval of time involved. When you’re new in town, explore like mad. If you’re about to leave a city, stick with the known favorites.

Infants with 80 years ahead are pure exploration— they try tasting everything. Old people, drawing on 70 years of experience, have every reason to pare the friends they want to spend time with down to a favored few. The joy of the young is discovering. The joy of the old is relishing.