The Conjunction Fallacy Does Not Exist

-38 curi 10 April 2011 10:35PM

The conjunction fallacy says that people attribute higher probability to X&Y than to Y.

This is false and misleading. It is based on bad pseudo-scientific research designed to prove that people are biased idiots. One of the intended implications, which the research does nothing to address, is that this is caused by genetics and isn't something people can change except by being aware of the bias and compensating for it when it will happen.

In order to achieve these results, the researchers choose X, Y, and the question they ask in a special way. Here's what they don't ask:

What's more likely this week, both a cure for cancer and a flood, or a flood?

Instead they do it like this:

http://en.wikipedia.org/wiki/Conjunction_fallacy

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.

Or like this:

http://lesswrong.com/lw/ji/conjunction_fallacy/

"A complete suspension of diplomatic relations between the USA and the Soviet Union, sometime in 1983."

"A Russian invasion of Poland, and a complete suspension of diplomatic relations between the USA and the Soviet Union, sometime in 1983."

These use different tricks. But both are biased in a way that biases the results.

By the way, this is a case of the general phenomenon that bad research often gets more impressive results, which is explained in _The Beginning of Infinity_ by David Deutsch. If they weren't bad researchers and didn't bias their research, they would have gotten a negative result and not had anything impressive to publish.

The trick with the first one is that the second answer is more evidence based than the first one. The first answer choice has nothing to do with the provided context. The second answer choice has something to do with the provided context: it is partially evidence based. Instead of taking the question really literally as to be about the mathematics of probability, they are deciding which answer makes more sense and saying that. The first one makes no sense (having nothing to do with the provided information). The second one partially makes sense, so they say it's better.

A more literally minded person would catch on to the trick. But so what? Why should people learn to split hairs so that they can give literally correct answers to bad and pointless questions? That's not a useful skill so most people don't learn it.

The trick with the second one is that the second answer is a better explanation. The first part provides a reason for the second part to happen. Claims that have explanatory reasons are better than claims that don't. People are helpfully reading "and" as expressing a relationship -- just as they would do if their friend asked them about the possibility of Russia invading Poland and the US suspending diplomacy. They think the two parts are relevant, and make sense together. With the first one, they don't see any good explanation offered so they reject the idea. Did it happen for no reason? Bad claim. Did it happen without an invasion of Poland or any other notable event worth mentioning? Bad claim.

People are using valuable real life skills, such as looking for good explanations and trying to figure out what reasonable question people intend to ask, rather than splitting hairs. This is not a horrible bias about X&Y being more likely than Y. It's just common sense. All the conjunction fallacy research shows is that you can miscommunicate with people and then and then blame them for the misunderstanding you caused. If you speak in a way such that you can reasonably expect to be misunderstood, you can then say people are wrong for not giving correct answers to what you meant and failed to communicate to them.

The conjunction fallacy does not exist, as it claims to, for all X and all Y. That it does exist for specially chosen X, Y and context is incapable of reaching the stated conclusion that it exists for all X and Y. The research is wrong and biased. It should become less wrong by recanting.

This insight was created by philosophical thinking of the type explained in _The Beginning of Infinity_ by David Deutsch. It was not created by empirical research, prediction, or Bayesian epistemology. It's one of many examples of how good philosophy leads to better results and helps us spot mistakes instead of making them. It also wasn't discovered by empirical research. As Deutsch explained, bad explanations can be rejected without testing, and testing them is pointless anyway (because they can just make ad hoc retreats to other bad explanations to avoid refutation by the data. Only good explanations can't do that.).

Please correct me if I'm wrong. Show me an unbiased study on this topic and I'll concede.