The Wisdom of Crowds

In this chapter, we’ll try an actual statistical experiment, where you can participate together with as all other Mathigon users.

When you click the button below, we'll show you a simple question, and you have 10 seconds to submit an answer. Do not try to calculate the answer – just guess using your gut feeling:

We'll return to this question shortly, to see how close your guess was to the actual answer, and how everyone else did. Before we do that, let's try a slightly different problem.

In this case, you'll have one minute to make a more precise estimate of the answer For example, we could guess how many jelly beans are in a single "layer" of the jar, and then multiply that number by the approximate number of layersheight of the jardiameter of the jat:

Now you have to make a prediction: Which of these two estimates do you think is more accurate?

Now

The answer might surprise you.

ACTUAL AMOUNT: XXX YOUR INITIAL GUESS: XXX A: AVERAGE OF ALL USER INITIAL GUESSES: XXX B: YOUR ROUGH CALCULATION: XXX

Turns out the average (mean) of all user guesses is pretty accurate!

Even though an individual guess might be way off, when we take many guesses from many different people and average them together we get a REALLY GOOD guess.

It’s kind of like magic and known as the wisdom of the crowd. It’s similar to what we covered in the last chapter on random sampling (link) where each human guess is like a random sample.

There might be some really ‘good guessers’ in the crowd, who happen to be closer to the answer, but the majority of people will probably be quite far off: some will overestimate the number of beans, while others will underestimate it. Luckily, these errors will cancel each other out. This is because for every large overestimate there is likely someone with a large underestimate. When we average these values together their average (mean) will be in the middle, near the good guesses.

That means that adding more and more guesses will make our prediction XXX [more accurate, less accurate].

As we increase the number of people in our crowd of guessers we will get a more accurate answer.

This phenomena was popularized in the 19th Century when Francis Galton asked people at a county fair to guess the weight of an ox. When he averaged those guesses he found that it was much more accurate than the guess of a single expert.

Let’s try this out one more time. Instead of an ox let’s try the biggest truck in the world (the BelAZ 75710). How heavy do you think it is?

YOUR ANSWER: XXX kg

[https://upload.wikimedia.org/wikipedia/commons/thumb/e/e2/BelAZ_75710.jpg/1280px-BelAZ_75710.jpg]

Here is the results:

AVERAGE USER ANSWER: _____

ACTUAL ANSWER: 360,000 kg

Not bad, the Mathigon users guessed within X% of the true answer!

BONUS CASE STUDY: The Challenger Accident

Another place we see the wisdom of the crowds in action is in the stock market. Stock prices represent a guess of the future value of a company. We can think of each investor who buys/sells stock as making a guess that the value should be “higher” or “lower”.

A famous example of this took place immediately after the tragic Challenger accident when the space shuttle crashes soon after take off.

At first, nobody knew what caused the accident, there were many different parts that could have failed and each was made by a different company. At this time investors who held stock in companies which made these parts had to make a quick decision, to sell or not. This is because the company which caused the accident would be hit with fines & bad publicity and would drop in value immediately.

Let’s have a look at the prices of the top 4 component suppliers to the Space Shuttle within hours of the accident:

Lockheed: -5% Marietta: -3% Rockwell: -5% Thiokol: -12%

Which company do you think created the part which caused the accident? XXX

It turns out the market was right to guess Thiokol. Weeks later it was confirmed that the component made by Thiokol was the cause. They manufactured a rubber seal which froze on take off causing it to fail. Here is a short clip of physicist Richard Feynman who identified the problem long after the market predicted it.

https://www.youtube.com/watch?v=8qAi_9quzUY

So while one of the greatest physicists of the 20th Century figured out the answer to this question in a few weeks, a collection of investors figured it out collectively much faster, in just hours.

Remember the wisdom of crowds next time you have a challenging answer to solve...it may just save you some time!