O/T The Allais Paradox

[TightEnd]

A long time ago I saw this, and once had to answer an exam question on it.

How would you approach this?



The Allais Paradox involves the choice between two alternatives:

Alternative A

89% chance of an an unknown amount
10% chance of £1 Million
1% chance of £1 Million

Alternative B

89% chance of an unknown amount (the same amount as in A)
10% chance of £2.5 million
1% chance of nothing


What is the rational choice?

 Does this choice remain the same if the unknown amount is £1 million?

If it is nothing?



NO GOOGLING....more Decision Puzzles to follow if this goes well.......

[Heid]

Gotta be A cause you have no chance of getting nothing.


That's MY rational choice

[Bongo]

I studied this at uni.

I can't remember much, but i'm guessing it has alot to do with how risk averse most people are.

[Heid]

I studied this at uni.

I can't remember much, but i'm guessing it has alot to do with how risk averse most people are.

Ahh I am a complete Wuss then

[The Baron]

I studied this at uni.

I can't remember much, but i'm guessing it has alot to do with how risk averse most people are.

So did I. I would go for (b), however I would go for (a) if the unknown amount was a million.

[12barblues]

Option B every time (assuming the unknown amounts in A and B are equal). It is about expected values isn't it?

But then it wouldn't be a paradox, so I must be way off beam........

[Bongo]

The paradox is the EV of B is higher but most people choose A because of the fear of the 1% chance of getting 0.

[TightEnd]

Bongo's on the right lines


there wasn't much interest in this, but the answer is as follows:

courtesy of the Doc (Me!)


Which choice is rational depends upon the subjective value of money. Many people are risk averse, and prefer the better chance of £1
million of option A.  This choice is firm when the unknown amount is £1 million, but seems to waver as the amount falls to nothing.  In the
latter case, the risk averse person favours B because there is not much difference between 10% and 11%, but there is a big difference between
£1 million and £2.5 million.

Thus the choice between A and B depends upon the unknown amount, even though it is the same unknown amount independent of the choice.  This
violates the "independence axiom" that rational choice between two alternatives should depend only upon how those two alternatives differ.

However, if the amounts involved in the problem are reduced to tens of pounds instead of millions of pounds, people's behavior tends to
fall back in line with the axioms of rational choice.  People tend tochoose option B regardless of the unknown amount.  Perhaps when
presented with such huge numbers, people begin to calculate qualitatively.  For example, if the unknown amount is £1 million the
options are:

   A. a fortune, guaranteed
   B. a fortune, almost guaranteed
      a tiny chance of nothing

Then the choice of A is rational.  However, if the unknown amount is nothing, the options are:

   A. small chance of a fortune (£1 million)
      large chance of nothing
   B. small chance of a larger fortune (£2.5 million)
      large chance of nothing

In this case, the choice of B is rational.  The Allais Paradox then results from the limited ability to rationally calculate with such
unusual quantities.  The brain is not a calculator and rational calculations may rely on things like training, experience, and
analogy, none of which would help in this case.  This hypothesis could be tested by studying the correlation between paradoxical
behavior and "unusualness" of the amounts involved.

If this explanation is correct, then the Paradox amounts to little more than the observation that the brain is an imperfect rational
engine.