# Information Cascades - How Many Rational People Can Make Logical Decisions and Yet Still Create a Bubble

When I say bubble, you likely conjure images of people speculating on real estate or stocks or tulips in your imagination. Like me, you might dismiss the folly of these bubbles as the collective action of a multitude of people who lose all rationality when bidding on these assets. But, as I learned from a recent interview with Brian Christian, bubbles can be created even when everyone acts rationally. This phenomenon is called an information cascade.

Here’s how it works. Suppose we have two opaque mason jars. One jar contains 23 red balls, 13 gray balls (majority-red). The other contains 23 gray balls and 13 red balls (majority-gray). I pick one of the two jars and place it before the a line of four people.

The first person steps up to draw a ball, and I instruct them,“Look at the color of the ball, but reveal the color to no one, and replace the ball. Given the color of the ball in your hand, share a guess of which jar is in front of you. Either majority-red or majority-gray.”

Suppose the first person pulls out a red ball. The first person should declare “majority-red,” since the odds are better that a red ball originate from the majority-red jar (66% vs 33%)

Suppose the second person also pulls out a red ball. She should also say “majority-red.”

Irrespective of the ball color the third person pulls, the third person will always say “majority-red.” If it’s a red ball, three red balls imply the majority-red jar. If it’s a gray ball, then it’s 2 reds and 1 gray, also imply a majority-red jar.

Every subsequent student is going to say majority-red, even if they are holding gray, because everyone before them will have said majority-red. This is the permanent and inevitable information cascade that can result when the first two balls are of the same color and everyone acts rationally. Read more about this theory and the math supporting it here.

Information cascades like these occur because we infer beliefs from others’ actions. If three acquirers are bidding \$250M to acquire a seed stage company, a fourth acquirer may infer from other bidders’ actions that the business is worth a quarter of a billion dollars, even if the fourth acquirer’s financial model doesn’t support it. A bidding war ensues.

These auction pressure dynamics lead to ever higher prices for assets. If the house down the corner sold for \$1M, and my house is newer and on a bigger lot, then it should be worth more than \$1M. Startup X raised at \$50M pre-money valuation with a revenue of \$500k. Mine is worth the more because it generates \$750k in revenue.

This continues ever higher until someone says “the jar is majority-blue.” That person, when attempting to dispel the fallacy of the bubble, acts irrationally. All the information in the market should lead her to another conclusion. But she begins to deflate the bubble by deciding the value of an asset based on her own information, her own models, her own assessment.

Information cascades don’t only happen in the financial markets. They also happen in meetings. Peter Drucker wrote the story of Alfred Sloan, the former CEO of GM, who entered a board meeting to discuss an important issue before the company. Sloan asked the opinions of his directors. When everyone agreed without comment, he immediately stopped the board meeting and said something along the lines of, “Since we’re all in agreement, it’s clear no one has considered the issue. Let us reconvene tomorrow after giving the matter appropriate thought.”

The obligation to dissent is the only way to combat information cascades.