Guess the number of M&M’s in the jar and win …

November 14, 2019

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We have all seen it at least once in our life: ‘Guess the number of M&M’s in the jar and win …’. Unfortunately, most of us have never been able to give an accurate guess. However, there exists a concept that can consistently yield accurate guesses. 
The wisdom of crowds is the concept that a large group of people has a higher collective intelligence than individual experts. This idea is applicable to a vast variety of instances including problem-solving, decision-making, forecasting, and policymaking. For example, some companies measure market sentiment via Twitter feeds. Data from individual tweets is aggregated to reflect the collective sentiment of all Twitter users about a certain market. By the wisdom of crowds concept the set of all Twitter users has a higher intelligence and therefore, the method yields an accurate measure of market sentiment.
We could also apply the wisdom of crowds concept to the M&M’s in the jar problem. Let a jar with 270 M&M’s be given. We proceed by asking a group of people to write down their guess of how many M&M’s are in the jar. We get the following results:

Person: Guess:
1 350
2 150
3 174
4 594
5 422
6 441
7 199
8 324
9 267
10 244

We get an average guess of 316,5 M&M’s which is close to the actual amount of 270 M&M’s. Note, however, that the accuracy of the average guess can be increased by asking a bigger group of people (e.g. > 100) what their individual guesses would be. Our guess would be the average guess of the group, thus allowing us to make an accurate prediction of the number of M&M’s in the jar.
There is, however, a more accurate wisdom of crowds method for a certain group of problems. This method utilizes the knowledge of the expert minority within a group to its full extent.

Surprisingly popular

The surprisingly popular method was developed by researchers at the Massachusetts Institute of Technology (MIT) for single-question problems. It uses the knowledge of the expert minority within a group to give more accurate results.
Consider the following case, we ask the following yes-no 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, this is not true, the capital of Australia is Canberra. Additionally, we ask the individuals in the group about what they think that most people will respond.
Suppose that we got the following results:
Is Sydney the capital of Australia? (yes-no question)
Yes: 65%
No: 35%
What do you think most people will respond? (most popular answer question)
Yes: 80%
No: 20%
The difference between the yes-no question and the most popular answer question is:
Yes: 65% – 80% = -15%
No: 35% – 20% = 15%
From the above we can conclude that the ‘no’ answer is surprisingly popular, since 15% is bigger than -15%. Note that we can divide the surprisingly popular method for yes-no questions into four simple steps:

  1. Ask a group of people a yes-no question
  2. Ask the group what they think will be the most popular answer
  3. Calculate the difference between the yes-no question and the most popular answer question.
  4. Determine which is the surprisingly popular answer.

By following these steps we were able to derive the correct answer to the question: Is Sydney the capital of Australia? In fact, this method is applicable to a wide variety of yes-no questions.
Now, we have discussed some methods for the wisdom of crowds concept and how they can be applied to real-life problems. The next time you encounter a M&M’s in a jar problem make use of the wisdom of crowds concept and the odds of making a correct guess might increase greatly. May the odds be in your favor.
Want to know more? Check out ‘Prediction by the Numbers’ on Netflix.

This article is written by Berke Aslan

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