Herding (Banerjee) Flashcards
Banerjee - Herding model
100 people are deciding between restaurants Archie’s (A) and Beth’s (B)
4 assumptions
Suppose 100 people are deciding between restaurants Archie’s (A) and Beth’s (B)
Prior belief: 51% for Archie’s
Each person gets one signal from a friend which is better
In reality, B is better, so 99 out of 100 people get a B signal
Assume
People pick in sequence
People see previous people’s actions but not their signals
Tie breaking rule exists
Info valued equally
Suppose the 1 person who heard A is better picks first (99 other get B signal)
What does the 2nd and 3rd person do?
Chooses A despite having B signal - since person 1 mustve had an A signal.
Weighs info equally so follows A
3rd person follows and chooses A despite also having a B signal, since the only thing they can know for sure is person 1 had an A signal, they dont know what person 2 had!! So all pick A. ALL 99 IGNORE THEIR OWN SIGNAL OF B! HERDING!
Why is herding bad (2)
Destorys information and discourages new experimentation
Leads to coordination on bad outcomes
Causes of herding (3)
Unobservability of signals - only knew the person 1’s signal
Sequential structure of choices - 1 after other
The existence of a tie-breaking rule favouring the wrong option
How to remedy this case?
Keep windows closed until first 10 people have chosen (they wouldve seen 9 signals to B! Becomes clear B is better)
THIS IS WHY INTERNET REVIEWS DONT PUBLISH UNTIL 5 REVIEWS! TO AVOID HERDING!
Banerjee also looked at continuous choice
Pick a point i, only one correct i*
Each individual received one signal of ik with probability a, correct with probability β.
Or get no signal with probability 1-a
Tie breaking rules:
Pick i=0 if no information, if indifferent between your own and other signals pick your own, if indifferent between other signals, pick the highest i
Intuition
If someone picks my signal, I know it is correct so should follow it immediately.
First person picks own signal if he has one. If not, picks i=0.
2nd picks own signal if has one, otherwise go with first signal.
If 2 follow 1. What does the 3rd know and do
3rd knows either they both had the same signal - so must be correct. (Rare but still a possibility)
Or , 2 had no signal so just followed 1
So person 3 dismisses his own signal and follows them, since there is a possibilty both have a correct signal and 3 has the wrong one. So creates a tie-breaker and follows them because of that possibility
Basically as soon as one i has been picked by 2 people, people dismiss their own signal and follow
When is the exception
If they see their signal has been chose at least once before
So how does herding start
Because of people without signals, who follow others (the 2nd person in the example; clouds decision for 3rd person: there becomes a chance that the first 2 got the same (although unlikely) but have to follow their option cos of that small chance
That was if 2nd had no info. If first person has no signal arrives before first person with a correct signal, entire population will chose the wrong option! unfortunately dismiss their own
2 possible Remedies
Let the first 1/(1-aB) people chose without observing previous choices, and so you should get one that has a correct signal
Pay people without a signal to choose later!
