Mutual knowledge, common knowledge, pluralistic ignorance

Publish Date: 
Sun, 06/05/2016 - 12:20

A new post on Terry Tao's blog talks about what's considered "common knowledge" in the context of the current US election:

A classic example arises from Hans Christian Andersens’ fable of the Emperor’s New Clothes: the fact that the emperor in fact has no clothes is mutual knowledge, but not common knowledge, because everyone (save, eventually, for a small child) is refusing to acknowledge the emperor’s nakedness. . . .

Trump is unfit to be president, and everybody knows it. But more people need to say so, openly.

This discussion closely echoes some old posts here on the work Dushoff, Akhmetzhanov and I did about pluralistic ignorance and how social norms change.

On thresholds and abrupt social change:

A community . . . with lots of people who would adopt the change if they expected enough other people to do it, but they aren't adopting it because they don't think there are enough people to satisfy their thresholds. Then someone finds a way to convince people that lots of other people feel the same way, and then they all become willing to do it.

On Pluralistic ignorance and thresholds:

Pluralistic ignorance - thinking that others do it because of personal preference . . . implies the belief that there isn't a low-conformity equilibrium, and in this way can prevent people from abandoning the norm. A public discussion, or something else that reveals people's preferences, can break them out of this trap.

In our 2013 paper, "Effects of mixing in threshold models of social behavior":

We show that the effects of considering the network can be decomposed into finite-neighborhood effects, and finite-mixing-rate effects, which have qualitatively similar effects. Both of these effects increase the tendency of the system to move from a less-desired equilibrium to the "ground state".

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