# 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!

Indeed:

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).