# Monthly Archives: January 2020

## Daniel Kahneman: Thinking, Fast And Slow, Deep Learning, And AI

Posted by on January 15, 2020 in cognitive science

## Conjunction Fallacies Abound

I’ve ranted about the conjunction fallacy before. Help me out, 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?

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

The majority of those asked chose option 2. However, the probability of two events occurring together (in “conjunction”) is always less than or equal to the probability of either one occurring alone—formally, for two events A and B this inequality could be written as Pr(A & B) < Pr(A) and Pr(A & B) < Pr(B).

For example, even choosing a very low probability of Linda being a bank teller, say Pr(Linda is a bank teller) = 0.05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = 0.95, then, assuming independence, Pr(Linda is a bank teller and Linda is a feminist) = 0.05 × 0.95 or 0.0475, lower than Pr(Linda is a bank teller).

Tversky and Kahneman argue that most people get this problem wrong because they use a heuristic (an easily calculated) procedure called representativeness to make this kind of judgment: Option 2 seems more “representative” of Linda based on the description of her, even though it is clearly mathematically less likely.

In other words, the representativeness bias (System 1) is making people answer when people should be using math (System 2).

There are a bunch of other instances of this:

Which is more probable?

1. God exists

2. God exists and cares about you

Which is more probable?

1. Jesus was crucified

2. Jesus was crucified and had twelve disciples

Which is more probable?

1. Organ A is responsible for the disease

2. Protein G in Organ A is responsible for the disease

Which is more probable?

1. Men assault/kill most people because men are violent

2. Men assault/kill women specifically due to misogyny

Remember what causes bias: We are biased because we use our moral intuitions to decide on something before using our more analytical brain, and we only use our analytical brain to defend our moral intuitions.

Chances are high that if some answer that should be a basic math problem upsets you, then you are defending your biases.

Take the last conjunction fallacy, that men assault women specifically due to misogyny. Already we are asserting a moral issue (misogyny) as the causal agent. Bias is already being prompted. But if men assault more people period due to men being more violent than women, there’s no need to introduce an additional factor when men assault women. Of course if men assault more people than women, the subset of people includes women. Hence the conjunction.

Now if it turned out that men assaulted/killed women more than men, an additional explanatory factor might be needed. This is not the case though.

Anytime you see an issue where the subset is being presented as more probable than its superset, you’re probably dealing with a conjunction fallacy. Indeed, if you want to nip this bias in the bud, always think about the possible supersets and their likelihoods.

Comments Off on Conjunction Fallacies Abound

Posted by on January 5, 2020 in cognitive science, religion

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