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


How much does cognitive dissonance contribute to the even distribution of bias?  (The "Data" in the question suggests an inverse effect.)
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).