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Following AND Leading in an Information Cascade

 

Information cascades were a recent topic discussed. An information cascade arises when the information that you can infer from the choices of others may be more powerful than your own private information, in which case it would in fact make sense for you to join others regardless of your own private information. People inevitably have the power to influence each other’s behavior and decisions.

Followership is something that was heavily emphasized, that once a person is influenced by seeing others make powerful choices, then they would submissively follow. However, one counterexample of how a person can both lead and follow in an information cascade is in the prisoner hat riddle. In this riddle, a group of prisoners are guaranteed freedom if they can successfully solve the following problem:

  • Prisoners are placed in a single-file line, facing forward, in size order, so that each prisoner can see everyone lined up ahead of themselves.
  • Prisoners cannot look behind themselves or step out of line
  • Each prisoner will have either a white or black hat, assigned randomly, and are not told how many there are.
  • Each prisoner will guess the color of their hat, starting from the tallest person in the back and moving forward.
  • Prisoners cannot say anything other than “black” or “white” or signal some other way like intonation or volume.
  • One mistake is permitted.

I will allow you, the reader, a chance to think of a solution!

The solution of this riddle illustrates that a followership-leadership duality is possible in an information cascade.

Media link: https://www.youtube.com/watch?v=N5vJSNXPEwA (Ted-Ed)

Blog post 2, edited 12/6 updating content and removing spoilers

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