The Possibility Effect: why lotteries and insurance exist
I recently finished reading Thinking Fast and Slow, a book on behavioral psychology and decision-making by Daniel Kahneman. One of the sections in Kahneman’s book is about choices — how people make decisions when faced with risk.
Many of us are familiar with the concept of loss aversion. When people are faced with an uncertain, risky outcome, then “losses loom larger than gains.” As Kahneman points out:
“In mixed gambles, where both a gain and loss are possible, loss aversion causes extremely risk-averse choices.”
As he continued to research loss aversion, Kahneman discovered a number of additional key insights. His insights were that (1) the prospect of losing a potential gain creates feelings of loss aversion, and (2) people may actually seek risks when facing near-certain losses. In other words, whether you are facing a gain or loss, and whether you think it’s high- or low-probability, influences your behavior.
Kahneman captures these insights in a concept called the Fourfold Pattern, which goes beyond loss aversion to show the different ways people respond to high- and low-probability events when they are either gains or losses.
In this 2x2 matrix, the top row contains scenarios that are likely to happen (high probability), either gains or losses. These scenarios correspond to the “Certainty Effect.” The bottom row contains scenarios that are unlikely to happen (low probability), either gains or losses. These scenarios correspond to the “Possibility Effect.”
Within each cell of the matrix, you have the following:
- an outcome (e.g. “95% chance to win $10k”)
- an emotion that is evoked (e.g. “Fear of disappointment”)
- the typical behavior (e.g. “RISK AVERSE”)
Let’s look at each cell in some detail:
High probability gain (“settle out of court”)
This is the situation that is captured in the top left cell of the matrix.
In this scenario, you face a likely gain. You have a 95% chance of gaining $10k. If someone offered you $9k with 100% probability, would you take it? If you’re a student of economics, you would say, “The expected value of my current situation is $9.5k = 95% & $10k. So why should I take $9k with 100% probability? It’s less than the $9.5k expected value.”
But many people would indeed take the $9k with 100% probability offer. Why? They would do so because they feel risk averse in this scenario. Even though the probability is small (5%), the potential loss of the entire $10k looms large. They are motivated by a fear of disappointment: “What if I don’t gain the $10k that is right within my grasp?” So what do people in this scenario do?
Here’s a real-life situation. Imagine that you’re the plaintiff in a civil case, and you believe you have a 95% chance of winning the case and an award of $10k. The defendant knows that they are likely to lose the case, so they offer an out-of-court settlement of $9k. The plaintiff would most likely take the settlement, even though it’s below the expected value ($9.5k) and the full amount they are very likely to receive ($10k).
High probability loss (“all in”)
This is the situation that is captured in the top right of the 2x2 matrix.
You are faced with a near-certain loss — you have 95% chance to losing $10k. But you have some hope — though only a slim 5% chance — of avoiding the loss.
What do you do? Do you “know when to fold,” take your losses and move on? Or, do you go “all in” with whatever you have remaining, in the hopes that you may recover the near-certain loss?
Most people, surprisingly, go “all in.” Here is what Kahneman had to say about this scenario:
“Many unfortunate human situations unfold in the top right cell. This is where people who face very bad options take desperate gambles, accepting a high probability of making things worse in exchange for a small hope of avoiding a large loss. Risk taking of this kind often turns manageable failures into disasters. The thought of accepting the large sure loss is too painful, and the hope of complete relief too enticing, to make the sensible decision that it is time to cut one’s losses. This is where businesses that are losing ground to a superior technology waste their remaining assets in futile attempts to catch up. Because defeat is so difficult to accept, the losing side in wars often fights long past the point at which the victory of the other side is certain, and only a matter of time.”
The next two cells of the matrix illustrate the Possibility Effect — the behavior of individuals when they believe that there’s even a small possibility of a large gain, or a large loss.
Low probability gain (“the lottery”)
This is the scenario captured in the bottom left cell of the 2x2 matrix.
You are faced with an unlikely gain — there’s a small chance that you will gain a significant reward of $10k. Given this hope of a large gain, you become more risk seeking. As Kahneman writes:
“The possibility effect in the bottom left cell explains why lotteries are popular. When the top prize is very large, ticket buyers appear indifferent to the fact that their chance of winning is minuscule. A lottery ticket is the ultimate example of the possibility effect. Without a ticket you cannot win, with a ticket you have a chance, and whether the chance is tiny or merely small matters little. Of course, what people acquire with a ticket is more than a chance to win; it is the right to dream pleasantly of winning.”
Combined with the overconfidence and over-optimism biases, the possibility effect for gains explains why so many people become entrepreneurs or start small businesses. Although only 66% of businesses survive their first two years, and only 50% survive beyond the first five, small business owners become risk seekers because they are motivated by the hope of large gains.
Low probability loss (“insurance”)
This final scenario is captured in the bottom right cell of the 2x2 matrix.
You are faced with an unlikely loss — there’s a small chance that you will lose the large amount of $10k. Given this fear of a large loss, you become risk averse. This is a flavor of the loss aversion behavior that many of us are familiar with. As Kahneman writes:
“The bottom right cell is where insurance is bought. People are willing to pay much more for insurance than expected value — which is how insurance companies cover their costs and make their profits. Here again, people buy more than protection against an unlikely disaster; they eliminate a worry and purchase peace of mind.”
This is why insurance, extended warranties, and protection plans exist. Even though the chance of a loss is small, if it happens it will be painful. Hence you’re willing to pay a small insurance premium to eliminate or reduce the risk.
So what? Why is this all important?
In the business world, we are often making decisions ourselves, or persuading others to give their support for decisions. It’s important to understand some of the biases and heuristics that we have that will affect our decision-making — especially when it comes to risk and probabilities.
The next time you are making a decision or an argument to persuade others, think about the situation. Could the Possibility Effect influence the decision? How should you frame your argument?
If the situation you face is a low-probability loss, pitch your proposal as “peace of mind” insurance. Why not pay a small premium to reduce or eliminate the risk?
On the other hand, if you face low-probability gains, you might observe the group’s tendency to be risk-seeking. If you disagree with the risk-seeking approach, call out the “lottery effect” in the group’s thinking.
By taking a bit more time to analyze the situation, we can make a better decision or more successfully persuade those whose support we need. Keep in mind the possibility effect, the reason why lotteries and insurance exist.
