Bias 15: The Allais Paradox

As a financial director, we have the choice to invest in:

Scenario 1:

  • Stock A where we have 11% of chance to earn €1M and 89% to earn nothing
  • Stock B where we have 10% of chance to earn €5M and 90% to earn nothing

Which one do we choose?

Scenario 2:

Now, we have the choice to earn €1M or to:

  • Invest in a stock that has a 10% chance to earn €5M
  • Invest in a stock that has an 89% chance to earn €1M and a 1% chance to earn nothing

What do we do?

Most of us have a certain bias towards investing in stock B and taking the €1M in the second scenario.

Why is it a bias?

From a mathematical point of view, we have:

Scenario 1 Scenario 2
Stock A: €110.000 Sure option: €1M
Stock B: €500.000 Stock: €1,39M

So that choosing to keep the €1M is not mathematically optimal. But let’s assume that as human beings we are attributing our own utility to monetary outcomes so that, for instance, u(1M)=0,5M, u(5M)=1M and by convention u(0)=0. But even in this case, we are not consistent!


Scenario 1 Scenario 2
Stock A: .11*u(1M) Sure option: u(1M)
Stock B: .10*u(5M) Stock: .10*u(5M)+.89*u(1M)

If we choose B over A, then u(5M)>1,1*u(1M)

In the second scenario, we have u(1M)> .10*u(5M)+.89*u(1M) so that u(1M)>1,1*u((M) which is in contradiction with our choice in the first scenario.

This bias is called certainty bias. According to recent research in neuroscience, when facing a lottery dilemma, we first consider the expected reward (activation of subcortical
dopaminoceptive regions: the putamen and striatum) and then (~1 s after) the risk ( activation of the striatum). This sensitivity to both expected reward and risk is not unique to financial situations. It is also observed in primates (Fiorillo et al.,2003; McCoy et al., 2003) and bees choosing among different flowers (Real, 1991).