I suspect respondents are answering different questions from the ones asked. And where the question does not include probability values for the options the respondents are making up their own. It does not account for respondents arbitrarily ordering what they perceive as equal probabilities. And finally, they may be changing the component probabilities so that they are using different probability values throughout when viewing the options.
The respondents are actually reading the probabilities as independent, and assigning probabilities such as this:
A: P(Accountant) = 0.1
C: P(Jazz) = 0.01
E: P(Accountant^Jazz) = P(Accountant) x P(Jazz) = 0.001, and you would expect the correct ranking
But if they are perceiving E as conditional then P(Accountant|Jazz) = P(Accountant^Jazz)/P(Jazz) =... (read 499 more words →)
I suspect respondents are answering different questions from the ones asked. And where the question does not include probability values for the options the respondents are making up their own. It does not account for respondents arbitrarily ordering what they perceive as equal probabilities. And finally, they may be changing the component probabilities so that they are using different probability values throughout when viewing the options.
The respondents are actually reading the probabilities as independent, and assigning probabilities such as this: A: P(Accountant) = 0.1 C: P(Jazz) = 0.01 E: P(Accountant^Jazz) = P(Accountant) x P(Jazz) = 0.001, and you would expect the correct ranking
But if they are perceiving E as conditional then P(Accountant|Jazz) = P(Accountant^Jazz)/P(Jazz) =... (read 499 more words →)