The conjunction fallacy under probability and betting instructions
Researchers have tried to keep subjects from committing the conjunction fallacy since Tversky and Kahneman discovered it in 1983. Betting paradigms (Bar-Hillel, 1993) have been used to force subjects to use a mathematical interpretation of "probability", but past experiments have either not involved actual betting or have had subjects bet on fictitious situations. In the current experiments half of the subjects were asked to decide which of 2 statements (about future events) had a higher probability while the other half were asked which statement they would prefer to bet on (in view of an actual payoff). The hypothesis was that while subjects in the probability condition would commit the conjunction fallacy, those in the betting condition would not. This hypothesis was not supported---there was not a significant difference between the numbers of conjunction fallacies committed by subjects in the two conditions in either of two experiments.
Sides, Ashley Ellen. "The conjunction fallacy under probability and betting instructions." (2000) Master’s Thesis, Rice University. https://hdl.handle.net/1911/17378.