Wisdom of the Crowds in “Who Wants to Be a Millionaire?”
https://www.telegraph.co.uk/culture/books/3620109/Always-ask-the-audience.html
The Wisdom of Crowds is useful in games such as “Who Wants to Be a Millionaire?” where players are given the option to ask the crowd to answer a question for them. Any random vote doesn’t mean much, but taken together, the collective wisdom of all the votes tends to be very accurate. Even when participants are asked to give a numerical answer to a question, the average answer of the crowd tends to be very accurate. For example, a Victorian scientist named Francis Galton asked people to guess the weight of an ox in order to prove how dumb they were, only to average the answers and find that the average answer was only .1 percent off from the correct answer.
The Wisdom of Crowds works great in situations like game shows, or making guesses about a topic most people know something about, but it shouldn’t be used to make serious predictions. Imagine if employees in a company were to collectively gamble on certain scenarios and use their odds to make decisions for the company. Or if scientists used the wisdom of crowds to predict the conditions of an experiment. Sometimes crowds do not have the necessary information to make a correct decision, even if the decision is an aggregate of all of the crowd’s choices.
In class, we talked about Wisdom of Crowds in the context of horse bettors. In particular, the crowd at the racetrack determines the state prices, and these odds are the average of the opinions in the crowd. As long as the opinions from the crowd are independent of each other, then the state prices do converge to the probabilities as the size of the crowd grows. Similarly, the likelihood that the crowd guesses answer correctly on “Who Wants to Be a Millionaire?” grows as the crowd gets larger. Also, it is important that all the guesses are equally weighted in both cases. If some guesses are weighted more heavily than others, there is a chance they could be inaccurate, which would change the average of the guesses.