Grocery Line Guessing
Which one is faster?:
the express lane with more customers who have fewer items
the regular lane with fewer customers with more items
It’s a puzzle we’ve all encountered in real life. Of course, there’s no one answer. There are too many variables. Maybe the express line only has one more person than the regular line, and the woman in the regular line has 100 items and a coupon to go with each one. Or, maybe the regular line has a couple people with 20 items, paying by credit card, while the express line has three old ladies paying by check.
Still, there must be some rule that could help one make the decision: Which line do I join?
Enter Dan Meyer, who offers a fairly easy answer: While there are variables, the regular lane is probably a better bet. Here’s the reason:
The manager backed me up on this one. You attract more people holding fewer total items, but as the data shows above, when you add one person to the line, you’re adding 48 extra seconds to the line length (that’s “tender time” added to “other time”) without even considering the items in her cart. Meanwhile, an extra item only costs you an extra 2.8 seconds. Therefore, you’d rather add 17 more items to the line than one extra person!
The real time suck is people paying. (As Meyer notes, the y-intercept is not even zero. It should take zero seconds to buy zero items — but even the pleasantries of a person passing through the line take a non-zero amount of time ["Hi! How are you today!"].)
While this makes a lot of sense when you think about it, it’s definitely not intuitive. After all, lots of people are sucked in by the express-lane fallacy. Trying to figure out why it’s so counterintuitive, I couldn’t help but think of the study I wrote about in this post.
In that post, I looked at the “length = number” strategy. That is, if you present a child younger than seven with two rows of items (buttons, for example) and ask them to say whether the two rows contain an equal number of items or not, you’ll probably find that they base their answer on the length of the rows — regardless of the actual number of items in each row. While adults tend to override this cognitive bias, fMRI studies have indicated that we have to work extra-hard not to fall back on it.
Thus, I would guess most people make a related calculation at the grocery store: length = time in line. Maybe in the future now you’ll be able to override this bias and check out faster than your unenlightened grocery-store compatriots.