Guilt, denial and groupthink

As is normal for a group of people who work together, every once in a while at our office an email gets sent out - usually by the boss - hilighting and chastising some egregious behaviour; be it anything from unprofessional conduct with a client to a lack of hygene in the bathroom.

A personal observation is that, usually without variance, every member of our staff (bear in mind, we are a small company of only 8 employees, all sharing a single office) replies with some form of indignation at the behaviour described. Seeing as at least one member of staff must be guilty of said behaviour, the fact that there is a universal display of scorn introduces an ostensible paradox.

From a purely cognitive point of view, this phenomenon never ceases to fascinate me, and I believe it treads into the realm of a branch of mathematics known as game theory.

When the original email enters the wilderness of the office network, the initial reaction of everyone involved is to speculate as to whom the guilty party might be; a zero-sum game is created. By responding with (sincere or pseudo) indignation, the individual believes himself to be removed from the pool of possible suspects. However, the consequences of this behaviour are purely mathematical and fully predictable.

As the pool of possible suspects shrinks, so does the likelihood increase that more individuals will react with this form of veiled denial in order to remove themselves from the pool and eliminate any chance of suspicion. Of course, the guilty party (or parties) must play this game too, in order to avert suspicion. This eventually leads to the absurd conclusion that everyone appears to be in equal disgust at behaviour in which at least one of the parties involved must surely have participated. Thus, everyone involved ends up looking even more foolish.

This is a variation of the so-called prisoner's dilemma that is occasionally found in game theory. As the dilemma itself illustrates, the best possible outcome for all parties involved is to accept, each and equally, some measure of the guilt and for no single individual to deny any burden of the guilt. In this way, the shared guilt amounts to less of a loss than the shared foolishness of the absurdity of a universal denial in the face of evidence to the contrary.

The dilemma, of course, is that none of the parties involved cooperates, even though it's in everyone's best interest to do so.

In this example we see mathematical principles being highlighted in our daily interactions, and not simply being relegated to the notebooks of mathematicians.