The conjunction and disjunction fallacies are famous for revealing the limits of human reasoning about probability.

This can be measured by telling people a short story about a character and then asking questions about the likelihood of certain statements about that character. Take a look at this story about Linda (which I’ve taken from Wikipedia):

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

Linda is a bank teller.

Linda is a bank teller and is active in the feminist movement.

It turns out that 85 per cent of people choose the second option. But the probability of two events occurring together (in
conjunction) is always less than or equal to the probability of one
of them alone.

This is the conjunction fallacy (humans show a
similar problem over the probability of one event OR another being
true, called the disjunction fallacy).

The question is how to
explain the problem humans have with this kind of reasoning. Until
now, psychologists have turned to classical probability theory to
study the concept of probability judgement error. This allows
them to build a mathematical model of human reasoning that
allows for errors in judgement.

But Jerome Busemeyer at
Indiana University and buddies have a different take. They say that
quantum probability theory leads to more realistic predictions about
the type of errors humans make.

“Quantum probability
theory is a general and coherent theory based on a set of (von
Neumann) axioms which relax some of the constraints underlying
classic (Kolmogorov) probability theory,” say the team.

That’s
an interesting insight, to say the least. And if it pans out, it
signals a fundamental shift in thinking about the brain.

What
Busemeyer and co are saying is that the principles of quantum
information processing, including the ideas of superposition and
interference, lead to better models of the way humans make
decisions.

What this idea needs, of course, is some kind
of testable hypothesis that differentiates it from classical models.
The team hint at this when describing how the principle of
superposition applies to thinking about voting habits, when a voter has to choose between two
candidates.

According to classical theory, before the vote is
cast, the voter is in a mixed state. But Busemeyer and co say that
thinking about the voter in a superposition of states is a better
model. That kind of thinking ought to lead to some testable
predictions.

Busemeyer and co are at pains to distance
themselves from research that uses quantum mechanics to model the
brain in an attempt to understand consciousness. and memory. “We
are not following this line,” they say. Instead they keep their
work far more abstract.

But inevitably the question will be
asked. If the principles of quantum information processing better
describe the way humans make decisions, what does that imply about the
way the brain works?

There’s no telling where this kind of thinking will lead.

Ref: arxiv.org/abs/0909.2789: Quantum Probability Explanations for Probability Judgment ‘Errors’

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