Going with the Crowd introduces a familiar scenario:
A few weeks ago, my family and I were wandering about in an unfamiliar part of the city where we live. We were getting hungry, so we started looking for a place to eat. We happened upon a block that had three restaurants in a row.All three restaurants served types of food that we enjoy. Although it was early in the evening, one was already quite crowded. Another had a couple at one table near the window. The third appeared to have no customers.
In such a situation, many people might think that there must be some reason why no one is at the third restaurant. Maybe there’s something wrong with it. The restaurant with just one couple might also appear questionable for the same reason.
I think you see where this is going:
So, in the absence of any additional information, the natural thing to do would be to join the crowd in the first restaurant. It must be a good, well-known restaurant. Higher quality brings more customers. Right?Suppose that the likelihood of someone choosing a restaurant is proportional to the number of people already in the restaurant. Given that all the restaurants are initially empty and that the first customer chooses randomly, what happens to the number of people that end up in the different restaurants?
Statistician Susan Holmes of Stanford University has created a Java applet that allows you to simulate such a situation.