I’ve been reading through the book Algorithms to Live By, and I thought it would be interesting to summarize or think of an application for each chapter since the book is about how algorithms influence or can be used in everyday decisions.
The first chapter is about the Optimal Stopping problem, which deals with deciding when to, well stop, given a decision that costs something over time. One example in the book is about hiring a secretary, or some other job candidate. According to the math, if you want to find the top candidate, you should reject the first 37% applicants in order to establish a baseline for the candidate quality, then accept the first candidate that outperforms the baseline.
I won’t try to go into the math too much, but this magic percentage is related to Euler’s number, e. Specifically, the number of candidates to initially reject is n/e where n is the number of candidates you plan to interview. Even more interesting about this is that: the probability of finding the best candidate converges to 37% as well (1/e).
But what does this really mean practically?
Let’s say you were buying a house, and you planned to look for 3 months, seeing 3 houses every week, that would be about 36 houses. So you would look at 36/e ≈ 13 houses, then choose the next house that’s better than the first 13. Which could be the next house, or you could have missed the best one already and are forced to accept the last house you see.
Even the best strategy sometimes yields bad results—which is why computer scientists take care to distinguish between “process” and “outcome.” If you followed the best possible process, then you’ve done all you can, and you shouldn’t blame yourself if things didn’t go your way.
– Brian Christian, Algorithms to Live By
No matter what the outcome is, you’ll know you gave yourself the best chance of succeeding. With decisions like this, even the ratings given to houses and candidates are subjective, and subject to change. Following a process (and believing it works) can help you feel good about your decision, without falling into FOMO or decision paralysis.