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Risk – The Known Unknowns

No object is more associated with the concept of risk than the coin. The coin has become the ultimate arbiter of chance.

Coin flips and risk

When the team captains come to midfield before the start of each Super Bowl the crowd quiets momentarily as the referee tosses a large coin into the air and then half the crowd will erupt in cheering because her favorite team wins the toss. The game hasn’t even started and already luck is on their side.

The connection between coin flips and risk is so ubiquitous that we even referred to an event whose outcomes are equally likely as a tossup. Coin flips present a pretty straightforward sort of risk. There are only two outcomes those outcomes are equally likely and most importantly we know that the process of flipping the coin is random. What happened in the last coin flip has no bearing on what happens on this coin flip.

Safe and risky options

So let’s see what happens in a simple laboratory experiment. Suppose that you were given a choice between a safe option and a risky option. The safe option is a sure one dollar. There’s no risk there. If you choose a safe option will get exactly 1 dollar
the risky option leads to a coin flip. If the coin lands heads will receive $2.50 but if the coin lands tales you’ll receive nothing.

Returning to a concept from the earlier lecture, the expected value of the risky option is $1.25, the average of those two equally likely outcomes. So, what should you choose? The safe or the risky option? If you are playing this game once there is no right answer, yes. The risky option has the higher expected value, but it’s outcomes are more variable and so what you choose could depend on your tolerance for risk.

But, suppose that you play this game 20 times one after another. If you chose the risky option every time you usually do better than someone who chose the safe option every time and you’d often do much better. More than 1/4 of the time you to earn an extra $10. Not bad for taking on a little risk.

Normal and pathological reactions to risk

Let me tell you what happened when two groups of participants played this game. Participants in group number one had what you might consider a pathological response to risk. They started off choosing the risky option, but as the game progressed they systematically move toward the safe option.

Even more strikingly, their behavior was influenced by regret over bad outcomes. If they chose the risky option and then lost, then they became much more likely to switch over immediately to the safe option. This first group earned about $20 on average write about what you would expect if you chose a safe option every time. Participants in group number two had what you might consider a healthy attitude toward risk.

They started off choosing the risky option and kept choosing it even if the coin flip started going against them. Their behavior stay pretty consistent over the course of the experiment and they were rewarded for their good choices earning about $25 on average. Interestingly the first group, those with a seemingly pathological response to risk were neurologically normal individuals recruited from advertisements in the local community.

That is people like you and me tend to show regret and risk aversion and they don’t earn as much money as it should. The second group those with a healthier approach to risk were individuals who had significant brain damage. They typically had experienced a stroke or tumor within a region of the base of the frontal lobes called the orbito-frontal cortex and they didn’t show normal regret.

But, why would this particular type of major brain damage help people to deal better with risk? It wasn’t because of brain damage in general there was another group of people in the same study with damage to different regions of the brain and that third group was just as bad at the task as a neurologically normal individuals. Something about regret provides an important clue for understanding decision-making under risk.