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73. The Allais Paradox

When rational choice theory meets human psychology

1
First Choice
2
Second Choice
3
Results

Which gamble would you choose?

A
100%
💰 100% Win $1,000,000
Certain: You walk away with $1M guaranteed
B
10%
89%
1%
🤑 10% Win $5,000,000
💰 89% Win $1,000,000
😰 1% Win $0
Expected: $1,390,000 (higher!)

Now choose between these gambles:

C
11%
89%
💰 11% Win $1,000,000
😐 89% Win $0
Expected: $110,000
D
10%
90%
🤑 10% Win $5,000,000
😐 90% Win $0
Expected: $500,000 (higher!)
~46%
Fell into the paradox
(Allais's 1952 study)
Leonard Savage
Nobel-caliber statistician
who fell into this trap

🎰 You've Been Allais'd!

You chose A and D — the most common pattern, and a violation of rational choice theory.

First Choice
?
Second Choice
?

Why This Is a Paradox

Look at the gambles again. In both cases, you're essentially choosing between the same core bet:

Your Core Bet
11% × $1M
vs
10% × $5M + 1% × $0
VS
What Changes
Q1: 89% → $1M (certain)
Q2: 89% → $0 (nothing)

The 89% is a "common consequence" — it's the same in both options of each question. According to expected utility theory's Independence Axiom, if you prefer one bet over another, adding or removing the same "common consequence" shouldn't change your preference.

The Independence Axiom

If you prefer A over B, then you should also prefer "A with a common consequence C" over "B with the same common consequence C."

But most people choose A (certain $1M) in Q1, then D (risky $5M) in Q2 — reversing their preference when the common consequence changes!

What This Reveals

The Allais Paradox exposes the certainty effect: humans dramatically overweight outcomes that are 100% certain compared to outcomes that are merely probable. The psychological difference between 99% and 100% feels massive, even though mathematically it's just 1%.

This discovery helped inspire Prospect Theory (Kahneman & Tversky, 1979), which won the Nobel Prize and became a foundation of behavioral economics.

The Lunch That Changed Economics

Paris, 1952

At a conference in Paris, French economist Maurice Allais approached Leonard Savage, the legendary statistician who had helped formalize expected utility theory. Over lunch, Allais casually presented Savage with these two questions.

Savage — "as knowledgeable about rational decision-making as anybody in the world" — considered the gambles carefully... and chose A and D.

When Allais pointed out the inconsistency, Savage was deeply disturbed. He had violated his own theory! The statistician who had mathematically proven how rational agents should behave had just demonstrated that even experts fall prey to cognitive biases.

The Aftermath

Allais published his paradox in Econometrica in 1953, but the economics establishment largely ignored it for decades. Expected utility theory was too elegant, too mathematically beautiful to abandon.

"If these were your preferences, you have just committed a logical sin and violated the rules of rational choice."
— Daniel Kahneman, Thinking Fast and Slow

It wasn't until 1979, when Kahneman and Tversky cited the Allais Paradox as "the best known counterexample to expected utility theory" in their landmark paper on Prospect Theory, that the economics profession began to take behavioral anomalies seriously.

Maurice Allais received the Nobel Prize in Economics in 1988 — 35 years after his paradox — "for his pioneering contributions to the theory of markets." The prize vindicated what lunch with Savage had revealed: humans are not calculating machines.