[Above: map showing average rents for one bedroom apartments in San Francisco, Feb 2013 - via Zumper.]

So I’ve signed a lease for a place in San Francisco – Nob Hill to be specific. The rent is utterly ridiculous, but I find solace in that the delusion is shared by the entire city. There is an acute shortage of residential housing in San Francisco, which means that listings turn over very quickly, sometimes in a matter of hours.

The velocity of turn-over presents an interesting problem. Since listings, especially the “good” ones, are taken off the market so quickly, as a renter you have to decide as if an apartment showing is a one-time decision. You can’t go and “think about it” because it will very likely be gone.

And because I am surrounded by very smart engineers, I learn that this is similar to a “Secretary Problem”:

The applicants are interviewed one-by-one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator can rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant.

When do you stop looking?

The secretary problem has a mathematically elegant solution, if you know exactly how many candidates you will interview in advance. The optimal strategy is to reject the first 1/e of candidates (which works out to be roughly less than a third) then pick the next one that is better than all previously interviewed candidates. This strategy has a 37% chance of finding the best candidate in the candidate pool.

Cool right?

True, but Useless

As cool as the strategy is, it was useless because I can’t actually know how big the pool of candidate rentals are. I cannot execute an optimal strategy. It did give me new ways of thinking about the problem though, i.e.:

1. Optimal is unreachable, let’s just shoot for good enough.
2. I should go see a bunch of places, establish a feel for the range of choice I face, and then just take the next one that is best of what I’ve seen so far.

I saw nine showings in three days, and took the ninth one. If nothing else, the secretary problem framework spares me from feeling terrible about making what is probably a suboptimal decision. Life’s not bad. Now I can focus on work.