While reading Daniel Kahneman's "Thinking, Fast and Slow" I've been stuck on the claim that Linda case and Dinnerware case have the same structure.
Linda is thirty-one 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 antinuclear demonstrations."
"Which alternative is more probable?
- Linda is a bank teller.
- Linda is a bank teller and is active in the feminist movement.
It is well-known that the majority of respondents chooses the second options (as most plausible, though the original question is about probability).
The Dinnerware case:
Being presented two sets of dinnerware:
Set A: 40 pieces / Set B: 24 pieces
Dinner plates: 8, all in good condition / 8, all in good condition
Soup/salad bowls: 8, all in good condition / 8, all in good condition
Dessert plates: 8, all in good condition / 8, all in good condition
Cups: 8, 2 of them broken / NONE
Saucers: 8, 7 of them broken / NONE
It is known that respondents tend to select Set B, though it is more beneficial to select set A.
Here is the question:
The dinnerware case is explained via the notion of 'averaging'. That is, person's System 1 (Kahneman's terminology) performs some kind of averaging and goes to conclusion, that as Set B items are not broken and in average cost more, then the whole Set B shall be preferred.
From the perspective of economic theory, this result is troubling: the economic value of a dinnerware set [...] is a sum-like variable." I.e. pure summation shall be performed where averaging and subsequent assessment is carried out.
The Linda problem and the dinnerware problem have exactly the same structure (??). Probability, like economic value, is a sum-like variable, as illustrated by this example: probability (Linda is a teller) = probability (Linda is feminist teller) + probability (Linda is non-feminist teller)" "System 1 averages instead of adding, so when the non-feminist bank tellers are removed from the set, subjective probability increases.
Here is my difficulty: I do not see how the 'averaging' notion applies to the Linda problem. When I myself think about Linda question, I do not realize that try to average something, I just want to construct something that fits my stereotypes. Otherwise, when I think about dinnerware, I agree that subconsciously try to maximize the average price of item.