Mutual vs Common Knowledge in course difficulty

A little bit of knowledge can be a powerful thing. There is a useful distinction that comes up a lot in game theory about knowledge. The two concepts are:

Mutual knowledge: all people in a group know about an event

Common knowledge: all people in a group know about an event, they all know that they know the event, they all know that they all know that they know the event, and so on ad infinitum.

The two concepts are very similar but not identical. There are fun ways to understand the distinction, and I have written about two puzzles that illustrate: Guess the number – a game theory puzzle, and Salem Witches – a math puzzle.

An example at Stanford

This week a news story came up about Stanford that I believe has a connection with mutual and common knowledge.

Here is the story via ESPN:

Stanford University stops distributing list of ‘easy’ courses that athletes had access to

Stanford has discontinued the practice of distributing a list of “courses of interest” only to student-athletes, according to a report by the “California Watch” investigative reporting project.

The course list, which was not advertised to the general student population, was widely regarded by Stanford student-athletes as an offering of easier classes. It was discontinued last week after reporters inquired about it, according to the report.

Question: what caused the university to change its policy?

I believe it had to do with a change from mutual knowledge to common knowledge.

Why? Before this news item, it was certainly the case the list of ‘easy classes’ was mutual knowledge. When I was a student at Stanford, I was aware about it as athletes mentioned it. Faculty probably had some idea too, and the administration of course knew about it. Some facts to corroborate this from The Stanford Daily:

Some faculty members said they didn’t believe the list harmed anyone — and may have helped fill their classrooms.

Art history lecturer Thomas Beischer, a former Stanford rower, said he welcomed the boost in enrollment brought by the inclusion of his class on the list.

While the list has an intended audience of student athletes, Lythcott-Haims said any Stanford student could have obtained a copy of the document, which was available only in hard copy from the offices of the Athletic Academic Resource Center — in the basement of the Arrillaga Center for Sports and Recreation.

Not mentioned is that employers and outsiders had some idea of this too. Employers could always look at a student’s transcript and judge that some classes would be easier.

So what changed when reporters asked about the story? It was an issue of knowledge:

Officials discontinued the list last week after student reporters working for California Watch began asking about it.

In other words, the University was worried that mutual knowledge of the class list would become common knowledge, which ironically happened anyway.

Once the game changed like this, Stanford elected to end the list to preserve its image.

This is just an official change–students can always talk and advisers can always keep their own non-public lists.

This is why the action feels like a strategic move about common knowledge.

If you’re curious, you can check out the course list on Scribd (also embedded below)

Course List