Ihor Kendiukhov

The common component, the 89% that was stripped out, was not psychologically or strategically inert.

In situation 1, it was providing certainty.

In situation 2, it was providing nothing.

Stripping it out changed the context in which the remaining options are evaluated, and a holistic reasoner, one who evaluates their total exposure rather than decomposing gambles into independent branches, should respond to that change.

This is precisely the point we made with the example in the introduction to Section 3.

If the common component C is a large safety net, you can afford to take more risk on the remaining branch.

If C is negligible, you should be more conservative

Your preference between A and B should depend on what else is in the package, because you are one agent facing the total distribution, not a collection of independent sub-agents each evaluating one branch in isolation.

The important distinction here is between the descriptive claim and the normative claim.

The descriptive claim, people violate independence in the Allays pattern, has been known since 1953 and is not controversial.

What is usually controversial is the normative status of this behaviour.

The standard treatment in economics and in much of the rationality community says, people violate the axiom, this is a bias, ideally they should be corrected.

The position I am defending is the opposite.

People violate the axiom because the axiom is too strong, their behavior reflects a rational holistic evaluation of the gamble's structure, and the correction, forcing independence-compliant preferences, would make them worse decision-makers, not better ones.

Subheading.

Ellsberg paradox.

The Ellsberg paradox involves a related but distinct phenomenon.

Ambiguity aversion.

The classic setup.

An urn contains 30 red balls and 60 balls that are either black or yellow in unknown proportion.