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.
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