DATA FROM Hey, John D., Gianna Lotito, Anna Maffioletti (2010) “The Descriptive and Predictive Adequacy of Theories of Decision Making under Uncertainty/Ambiguity” Journal of Risk and Uncertainty 41, 81–111. Also used by Kothiyal, Amit, Vitalie Spinu, & Peter P. Wakker (2014) “An Experimental Test of Prospect Theory for Predicting Choice under Ambiguity” Journal of Risk and Uncertainty 48, 1-17. Reproduced here with permission of the owners of this data set: John D. Hey, Gianna Lotito, & Anna Maffioletti The colors below are as in the paper by Hey et al. In the paper by Kothiyal et al., the colors blue and yellow were interchanged throughout. That is, the color blue below corresponds with the color yellow in Kothiyal et al., and the color yellow with the color blue. We thank Giacomo Lanzani for having provided some corrections. 1. DESCRIPTION OF THE EXPERIMENT The bingo blower used in the experiment contained pink, yellow and blue balls in 0.2, 0.3, and 0.5 proportions. There were three treatments (between subjects), with a total number of 10, 20, and 40 balls in the bingo blower, respectively: Treatment 1: 2 pink, 3 yellow, 5 blue Treatment 2: 4 pink, 6 yellow, 10 blue Treatment 2: 8 pink, 12 yellow, 20 blue Subjects were not informed about these numbers but could watch the bingo blower. The more balls in total, the harder it was for subjects to guess the proportions, and the more ambiguity they perceived. In Treatment 1, it is actually possible to count the balls of each colour — so this is a situation of risk. In Treatment 2, it is just about possible to count the number of pink balls and begin to guess the number of yellow balls but it is impossible to count the number of blue balls. In Treatment 3 it is impossible to count the balls of any colour. Recorded videos of all three treatments are available at: http://www.luiss.it/hey/ambiguity/1st.avi http://www.luiss.it/hey/ambiguity/2nd.avi http://www.luiss.it/hey/ambiguity/3rd.avi Only three possible outcomes were considered (-$10, $10, and $100). Each subject made 162 choices between pairs of prospects, which basically involved all nontrivial choices, with one choice randomly selected and played for real at the end of the experiment. For each theory, 135 choices were used for fitting (train set) and the remaining 27 choices were used as a prediction (test) set. The questions what were used as a test set are: 1, 4, 5, 11, 12, 30, 46, 56, 66, 78, 81, 86, 89, 95, 96, 98, 100, 108, 111, 112, 114, 133, 141, 143, 146, 157, 161 There were 48 subjects recruited - 15 in Treatment 1, 17 in Treatment 2 and 16 in Treatment 3. The subjects were paid a total of £2,130, on average £44.37 per subject. Subjects were recruited using the ORSEE (Greiner 2004) software and the experiment was conducted in the EXEC laboratory at the University of York using purpose-written software written in Visual Basic 6. 2. CODEBOOK OF VARIABLES Question: Question ID (1-162) Subject: Subject ID (1-48) Treatment: Treatment ID (1-3) Choice: Subjects' choices, either "L", "R", or "I" (indifferent) Test/Fit: Whether used for testing or for fitting Lp: Outcome of lotery L if event "pink" occurred Ly: Outcome of lotery L if event "yellow" occurred Lb: Outcome of lotery L if event "blue" occurred Rp: Outcome of lotery R if event "pink" occurred Ry: Outcome of lotery R if event "yellow" occurred Rb: Outcome of lotery R if event "blue" occurred 3. DATA Question, Subject, Treatment, Choice, Test/Fit, Lp, Ly, Lb, Rp, Ry, Rb 1, 1, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 2, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 3, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 4, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 5, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 6, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 7, 1, L, TEST, -10, 10, -10, -10, -10, 10 1, 8, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 9, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 10, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 11, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 12, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 13, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 14, 1, R, TEST, -10, 10, -10, -10, -10, 10 1, 15, 1, L, TEST, -10, 10, -10, -10, -10, 10 1, 16, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 17, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 18, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 19, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 20, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 21, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 22, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 23, 2, L, TEST, -10, 10, -10, -10, -10, 10 1, 24, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 25, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 26, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 27, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 28, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 29, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 30, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 31, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 32, 2, R, TEST, -10, 10, -10, -10, -10, 10 1, 33, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 34, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 35, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 36, 3, L, TEST, -10, 10, -10, -10, -10, 10 1, 37, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 38, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 39, 3, L, TEST, -10, 10, -10, -10, -10, 10 1, 40, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 41, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 42, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 43, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 44, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 45, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 46, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 47, 3, R, TEST, -10, 10, -10, -10, -10, 10 1, 48, 3, R, TEST, -10, 10, -10, -10, -10, 10 2, 1, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 2, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 3, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 4, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 5, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 6, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 7, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 8, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 9, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 10, 1, L, FIT, -10, 10, -10, -10, -10, 100 2, 11, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 12, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 13, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 14, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 15, 1, R, FIT, -10, 10, -10, -10, -10, 100 2, 16, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 17, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 18, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 19, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 20, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 21, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 22, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 23, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 24, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 25, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 26, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 27, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 28, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 29, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 30, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 31, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 32, 2, R, FIT, -10, 10, -10, -10, -10, 100 2, 33, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 34, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 35, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 36, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 37, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 38, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 39, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 40, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 41, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 42, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 43, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 44, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 45, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 46, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 47, 3, R, FIT, -10, 10, -10, -10, -10, 100 2, 48, 3, R, FIT, -10, 10, -10, -10, -10, 100 3, 1, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 2, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 3, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 4, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 5, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 6, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 7, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 8, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 9, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 10, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 11, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 12, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 13, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 14, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 15, 1, L, FIT, -10, 10, -10, 10, -10, -10 3, 16, 2, R, FIT, -10, 10, -10, 10, -10, -10 3, 17, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 18, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 19, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 20, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 21, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 22, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 23, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 24, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 25, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 26, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 27, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 28, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 29, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 30, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 31, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 32, 2, L, FIT, -10, 10, -10, 10, -10, -10 3, 33, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 34, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 35, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 36, 3, R, FIT, -10, 10, -10, 10, -10, -10 3, 37, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 38, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 39, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 40, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 41, 3, R, FIT, -10, 10, -10, 10, -10, -10 3, 42, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 43, 3, R, FIT, -10, 10, -10, 10, -10, -10 3, 44, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 45, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 46, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 47, 3, L, FIT, -10, 10, -10, 10, -10, -10 3, 48, 3, L, FIT, -10, 10, -10, 10, -10, -10 4, 1, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 2, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 3, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 4, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 5, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 6, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 7, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 8, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 9, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 10, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 11, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 12, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 13, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 14, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 15, 1, R, TEST, -10, 10, -10, 10, -10, 10 4, 16, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 17, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 18, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 19, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 20, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 21, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 22, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 23, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 24, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 25, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 26, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 27, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 28, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 29, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 30, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 31, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 32, 2, R, TEST, -10, 10, -10, 10, -10, 10 4, 33, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 34, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 35, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 36, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 37, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 38, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 39, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 40, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 41, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 42, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 43, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 44, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 45, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 46, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 47, 3, R, TEST, -10, 10, -10, 10, -10, 10 4, 48, 3, R, TEST, -10, 10, -10, 10, -10, 10 5, 1, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 2, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 3, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 4, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 5, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 6, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 7, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 8, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 9, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 10, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 11, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 12, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 13, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 14, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 15, 1, R, TEST, -10, 10, -10, 10, -10, 100 5, 16, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 17, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 18, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 19, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 20, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 21, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 22, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 23, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 24, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 25, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 26, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 27, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 28, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 29, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 30, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 31, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 32, 2, R, TEST, -10, 10, -10, 10, -10, 100 5, 33, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 34, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 35, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 36, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 37, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 38, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 39, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 40, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 41, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 42, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 43, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 44, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 45, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 46, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 47, 3, R, TEST, -10, 10, -10, 10, -10, 100 5, 48, 3, R, TEST, -10, 10, -10, 10, -10, 100 6, 1, 1, R, FIT, 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31, 2, L, FIT, 10, 100, 100, 100, 10, 100 153, 32, 2, L, FIT, 10, 100, 100, 100, 10, 100 153, 33, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 34, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 35, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 36, 3, R, FIT, 10, 100, 100, 100, 10, 100 153, 37, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 38, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 39, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 40, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 41, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 42, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 43, 3, R, FIT, 10, 100, 100, 100, 10, 100 153, 44, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 45, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 46, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 47, 3, L, FIT, 10, 100, 100, 100, 10, 100 153, 48, 3, L, FIT, 10, 100, 100, 100, 10, 100 154, 1, 1, R, FIT, 100, 10, -10, 100, -10, 10 154, 2, 1, R, FIT, 100, 10, -10, 100, -10, 10 154, 3, 1, R, FIT, 100, 10, -10, 100, -10, 10 154, 4, 1, R, FIT, 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