In many situations in life we have to make choices between actions which do not have a sure outcome. In decision making theory and psychology these actions with uncertain outcomes are often distilled to “gambles”. A “gamble” has at least two potential outcomes and each outcome has a probability of occurring. A typical example is a gable where with 50% chance you win 10 Euros and with 50% chance you win nothing.
I don’t intend to bore you with too much information on gables used in decision making research. At the same time, you have noticed something, namely that in each gamble there are numbers involved. As far as the outcomes are concerned, usually (when talking about small amounts) people have no trouble understanding what, for example, 10 Euros mean. After all 10 Euros are 10 Euros and that is it.
When it comes to probabilities, however, things are not that clear. Of course in the example presented above 50% chance is relatively easy to understand – a flip of a coin. The situation changes dramatically when probabilities are less easy to translate into vivid examples. For example a gamble is as follows: 23% Chance to win 40 Euros, 58% chance to win 3 Euros, 19% chance to win nothing. As you can easily see, things are a bit more complicated.
Leaving a bit the world of gables in decision making research, there is a universal truth that people are not good judges of probabilities. I’d like to present to you two nice psychological effects with regard to assessing probabilities. In order to do so we have to go back to the world of gambles. Imagine the following options (two gambles).
The FIRST Gamble is 61% chance of winning 65.000 Euros and 39% chance of winning 0.
The SECOND Gamble is 63% chance of winning 60.000 Euros and 37% chance of winning 0.
Which one of these two gambles would you like to take? If you are like most humans you would go for the FIRST one.
Now let’s change the game a bit… Consider the following two gambles:
The FIRST Gamble is 98% chance of winning 65.000 Euros and 2% chance of winning 0.
The SECOND Gamble is 100% chance of winning 60.000 Euros and 0% chance of winning 0.
Which one of these two gambles would you like to take? If you are like most humans you would go for the SECOND one.
What has happened here is called the "Allais Paradox." Your preference has changed in the second choice despite the problem being the same. In the second choice each wining probability was increased with 37 percentage points. In essence the problem is the same in both cases of choosing.
The fact that you have changed your preference is a serious violation of normative economics and assumptions of rationality. Don’t worry; no one will punish you for this.
What has happened is called also the certainty effect. In the first situation when the outcomes of both gambles were risky (with a probability) you preferred the higher outcome (65.000) with the smaller probability of wining (61%). When the smaller outcome (60.000) became certain you preferred the sure thing over the risky option of winning 5000 Euros more.
The example above is a very good example for also the effect of “risk aversion”. If we compute the objective values of the two gables, the first gamble has the following value: 65.000 *98% = 63700. The second gamble has the value of 60.000. In normative economics terms, you gave up 3700 euros… not very smart, an economist would say.
The essence of the certainty effect and of risk aversion is that when it comes to winnings we prefer a sure smaller outcome than a bigger risky one.
Another very interesting effect is that of “Possibility effect” and it has its roots in the same inability to accurately judge probabilities. The possibility effect represents the overestimation of very small probabilities.
Small probabilities are either ignored or highly overestimated. Small probabilities that are ignored are in essence rare events that you don’t even consider or think of. One example is being struck by lightning. In every storm there is a very small chance of being struck by lightning, but most people never think about it… especially the ones playing golf in a thunder storm.
At the same time, there are other very small probabilities that are highly overestimated. One example is playing the lottery. The probability of winning is negligible, but still people play. In the negative outcomes domain things are even worse than in the case of a lottery. For example people oppose the building of nuclear power plants due to the risk they pose. At the same time, nuclear power plants are in fact very safe (well… the soviet technology ones are less safe). Similarly for airplane crushes, people overestimate the danger of flying with an airplane.
The overestimation of very low probabilities is mainly due to the availability in memory of a rare event occurring. We have heard news about people winning the lottery; we have readily in mind an instance of an airplane crushing and so on. This is what makes us envision the possibility of a rare event occurring.
Even events on which we do not have information on are overestimated. Let’s take the example of a vaccination campaign among children. The vaccine prevents a common and very dangerous disease and has 0.00001% chances of killing the child that has received the shot. We have never heard of people dying of this vaccine, but we can imagine easily a dead child.
A side effect of the possibility effect is that people are really bad at comparing very small probabilities. For example a probability of 0.00001% (which means 1 in 10 millions) is perceived very similar to a 0.0001 (which means 1 in 10 thousands) … yes, I’ve tricked you by not adding the “%” sing at the end of the numbers.
In objective terms a probability of 1 in 10 million is much better than a probability of 1 in 10 thousand when it comes to bad events… it’s 1000 times better in fact. People, however, do not perceive this difference because in the mind there is a representation of the 1 suffering or worse.
To sum up, in general people are bad estimators of probabilities. We like sure things – certainty effect – even if they are worse than risky options. We overestimate the very small probabilities because rare events are possible.