Note: This article is part of a multi-part series called ‘Berke Revisits’ in which Berke looks back at old articles that he has written, and sheds some perspicacity on ideas, thoughts, and concepts of the old articles, all wrapped in a nice, easy to read, format.
You are strolling through the mall with your parents, about 10 years of age. Looking around: vivid imagery of storefronts, piles of clothing, a contingent of people, and suddenly, out of nowhere, there she is: the promotional girl. She is selling a product for a well-known chocolate brand and tells you that they have a promotional action: guess the number of chocolates in the jar and win a year worth of chocolate. Of course, as a young child, you want to win, so you make a wild guess: 120 chocolates. Sadly, you’re wrong, the ‘true’ number of chocolates in the jar is closer to 250, and you think to yourself: is there a better method to estimate the number of chocolates in the jar? 8 years go by, and now you are fresh out of high school and looking to challenge yourself intellectually, you are studying econometrics. And indeed, as you go through your statistics courses, you figure, there must be a better way to estimate the number of chocolates in the jar. Well, this article will be entirely dedicated to teaching you a method, where you can consistently estimate, the ‘number of X in Y’ type of questions, using the ‘Wisdom of Crowds’.
Wisdom of crowds
The wisdom of crowds is based on the ideal, that we as humans, collectively are far more intelligent, than individually. Of course, this is an ideal, although it is true, in some scenarios it may be false (i.e. when everyone in the populous at hand has severe cognitive limitations). In this article, we assume that we live in a world, where this ideal is true. We can apply the wisdom of crowds to nearly any situation in real-life, from problem-solving and policymaking, to forecasting and decision-making. In fact, we use it commonly, for example, when solving problems in a team of people, or when we aggregate Tweets from Twitter users to get the collective sentiment of all invested Twitter users on a certain topic. By the wisdom of crowds principle, we as a team, have vastly, more capable, problem-solving skills than an individual expert, and hence we develop a better solution. Likewise, our aggregated opinions on Twitter are a more accurate measure of sentiment of amongst the Twitter users, than the opinion of a single expert.
Now, as we progress with the article, you might notice the following: we can apply the wisdom of crowds to the number of chocolates in the jar problem. To test this, I bought a big jar and put a lot of chocolate in it. Then I asked a few friends and roommates the following question: how much chocolates are there in the jar? The results were as follows:
We have 10 people partaking in the experiment, so N = 10, which is relatively small, the bigger the group that you ask the question, the more accurate the estimate will be. Here, from an econometrics perspective, we can view the process of getting an estimate using the wisdom of crowds, as the estimator, and the guess, as the estimate (i.e. similar to the OLS, GLS, and MLE estimator, etc.). Our guess would be the mean of all the predictions of the individuals partaking the experiment: 59 chocolates. Indeed, we find that this is relatively close to the true value of 60.
You would be surprised to hear the following: there is a more accurate method to yield accurate predictions, the ‘surprisingly popular’ method. This method utilizes the knowledge of the expert minority within a group to yield more accurate predictions. The method was developed by researchers from the MIT (Massachusetts Institute of Technology) for single-question problems. Funnily, the method itself consists of two questions:
- First, a simple yes/no question is asked to the experimental group.
- Next, the experimental group is asked to determine the most popular answer.
- The difference in frequency between the yes/no answer and the most popular answer is calculated.
- The surprisingly popular answer is determined.
This may seem vague at first. To clarify, let us give a first-hand encounter of how the surprisingly popular method can be applied, albeit not necessarily to the type of question of the ‘chocolates in the jar’.
Consider the following question: is Sydney the capital of Australia? Many people tend to think that Sydney is the capital of Australia, due to its size and historical significance. However, the capital of Australia is Canberra. Suppose we get the following results:
- Is Sydney the capital of Australia?
- What do you think that most people will respond (i.e. most popular answer)?
The difference in frequency between the yes/no answer and the most popular answer is calculated:
Yes: 65% – 80% = -15%
No: 35% – 20% = 15%
From the above calculations, we infer that ‘No’ is the surprisingly popular, and indeed, correct answer (i.e. 15% > -15%). This method is applicable to a wide variety of yes/no questions.
To conclude, in this article I have discussed to methods to make more accurate guesses about topic you don’t necessarily now everything about, by utilizing the collective intelligence of others around you. As you have come this far, you now know when to apply which method, the general wisdom of crowds method, for almost anything, and the surprisingly popular method for yes/no questions. May the odds be in your favor!