Photo by Don Norman

This problem was originally investigated by usability expert Don Norman, and reworded into the form of a question by Gil Milbauer.

In an attempt to provide a mechanism where someone is not left in a situation with no toilet paper, some establishments have installed dual toilet paper dispensers. The question is, if there are unequal amounts remaining on each roll, which one should you pull your toilet paper from? Should it be from the larger roll or from the smaller roll?

[Look at the picture and think of your answer before you read on.]

As it turns out, everyone should pull from the smaller roll first until it is used up. The larger roll is a backup for when the smaller roll runs out of paper. After all, we don’t want to be stranded without any toilet paper. Then, when the smaller roll is empty, it can be replaced and act as the backup for the other roll.

Ironically, there is something in our human nature that directs most people to pull from the larger toilet paper roll. Don Norman’s analysis observes this:

The most natural… was to reach for the larger roll. Alas, consider the impact. Suppose we start with two rolls, A and B, where A is larger than B. With algorithm large, paper is taken from A, the larger of the two rolls until its size becomes noticeably smaller than the other roll, B. Then, paper is taken from B until it gets smaller than A, at which point A is preferred. In other words, the two rolls diminish at roughly the same rate, which means that when A runs out of paper, B will follow soon thereafter, stranding the user with two empty rolls.

Algorithm small turns out to be the proper choice. With algorithm small, paper is always taken from A, so it gets smaller and smaller until it runs out. Then paper is taken from roll B, which is full size at the time of the switch.

Gil Milbauer says, “This is one of many cases where a misguided egalitarian tendency (‘I think I’ll use the roll with more paper because then they’ll be more equal…’) leads to unintended bad consequences.”

Who knew you had think about using toilet paper?