# Thinking Fast and Slow: Similarity of Linda problem and Dinnerware case

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 problem:

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.

Then,

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.

• Pavel - I couldn't explain how this question was unclear to me, so I went ahead and provided an answer to help illustrate the ambiguity. I will certainly delete it, if its interpretation is way off. Please let me know! Aug 1, 2017 at 19:25

## Question Restatement:

It seems that "have exactly the same structure" is actually a reference to whether the underlying syllogisms are similar - in both research designs.

Another assumption: Given the absence of a quote from Daniel Kahneman's, "Thinking, Fast and Slow" - the question seems to be hoping for answers that will make an inference as to the goal of the questions/research. Otherwise, this would be moot as Kahneman probably explains in context.

## Possible Answer - Identifying Bias when Rational Responses aren't Possible:

Both research designs exhibit the same challenge to BOTH a respondent, and a researcher -

"What conclusions are they inclined to, (bias) - when it is impossible to respond reasonably?" (E.G., like be faced with a false dilemma logical fallacy).

The first tests Respondent's behavior; the second tests Researcher's behavior.

## The Linda Problem - Measuring Respondents:

In the first case, the question speaks about a "philosopher", and an expectation that they would be "objective" in their role as a banker. Regardless, a rationally minded respondent would immediately notices the absence of an obvious third answer, "None of the Above". Obviously, "Probability cannot be inferred."

Note: Because respondents feel a generous inclination to "help" the researchers - only a very small number of respondents are likely to protest the validity of the test.

## The Dinnerware Case - Measuring Researchers:

In the second case, the question is framed computationally, seeking a rational answer. Regardless, a rationally minded researcher immediately notices the absence of an obvious third explanation, "Set Theory" ... Obviously, "Cups" rings "dissonant" and does not have as strong a connection as the others do. So, the research design wrongfully disregards the primal valuation of "belonging" - which might have a higher valuation than "market value", and even "utility".

Note: Because researchers feel an obligation to make SOME inference - only a small portion might protest the validity of the test.

## Conclusion:

In other-words, I feel that the similarity between the designs is not at all about "averaging" or "valuation" - but their similarity is due to the "dilemma" that both researchers AND respondents are faced with - when confronted with an irrationality:

1. How much does cognitive dissonance contribute to the even distribution of bias? (The "Data" in the question suggests an inverse effect.)
2. And, if there is no even distribution of bias - when a rational answer cannot reasonably be provided, (given the logical errors of the circumstance) - then what biases do people tend towards? (The "Data" in the question suggests a universal bias towards "belonging, association", rather than rationality, personal values, etc.)

It would be very interesting to see the full implementation of this instrument - as it might inform political campaigns, (IMHO).

If the data from the two questions here is actually correct - then it might be consistent with what we observe in politics, (and relationships, etc).