Suppose you provide a statement such as "In 1984, the number of days that reached a high temperature of at least 75F in St. Louis was at least 155" and you wish to know how confident the participant is of the veracity of the assertion. I.e., you would like to know what probability she assigns to the statement being true. How would you do this in an incentive compatible manner, similar to part (a)

above? Hints: I again recommend using a set of binary choices. Let all payments to the participant be either High (say $10) or Low (say $0). One item in each choice pays High if it turns out that the statement in question is indeed true (assume the experimenter can reveal the truthfulness of the statement definitively once the questions are answered). The other item should be an objective lottery that assigns certain probabilities to High and Low, and these probabilities are what you should vary across choices.