Table 4. The 60 Problems Studied in Experiment 3 (the competition set).
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B-rate | |||||||||||||||||
Option A | Option B | Lottery | No-FB | With-FB | |||||||||||||
Prob | H | pH | L | Hb | pHb | Lb | Shape | Num | Corr | Amb | rb1 | rb2 | rb3 | rb4 | rb5 | ||
91 | 7 | 1 | 7 | 16 | 0.1 | 10 | 0 | - | 1 | 0 | 0 | - | 0.92 | 0.96 | 0.99 | 0.99 | 1 |
92 | 8 | 0.8 | -37 | 102 | 0.2 | -29 | 0 | - | 1 | 0 | 0 | - | 0.39 | 0.28 | 0.35 | 0.31 | 0.32 |
93 | 5 | 1 | 5 | 103 | 0.1 | -9 | 1 | L-skew | 4 | 0 | 1 | R-skew | 0.56 | 0.48 | 0.44 | 0.33 | 0.3 |
94 | 7 | 1 | 7 | 6 | 0.75 | 1 | 0 | - | 1 | 0 | 0 | - | 0.1 | 0.04 | 0.02 | 0.03 | 0.02 |
95 | -3 | 0.05 | -9 | 42 | 0.4 | -24 | 1 | L-skew | 6 | 1 | 0 | R-skew | 0.72 | 0.6 | 0.57 | 0.57 | 0.57 |
96 | 35 | 0.5 | -47 | -10 | 0.75 | -15 | 0 | - | 1 | 0 | 0 | - | 0.3 | 0.34 | 0.37 | 0.34 | 0.31 |
97 | 10 | 1 | 10 | 45 | 0.2 | -5 | 0 | - | 1 | 0 | 0 | - | 0.22 | 0.14 | 0.27 | 0.24 | 0.21 |
98 | 94 | 0.5 | -40 | 36 | 0.75 | -21 | 2 | Symm | 7 | 0 | 0 | Symm | 0.51 | 0.45 | 0.43 | 0.44 | 0.45 |
99 | 22 | 1 | 22 | 44 | 0.4 | 15 | 2 | Symm | 5 | 0 | 0 | Symm | 0.65 | 0.74 | 0.75 | 0.71 | 0.71 |
100 | 18 | 0.6 | -29 | -1 | 1 | -1 | 0 | - | 1 | 0 | 0 | - | 0.54 | 0.46 | 0.5 | 0.54 | 0.53 |
101 | 28 | 1 | 28 | 73 | 0.05 | 27 | 2 | Symm | 3 | 0 | 0 | Symm | 0.83 | 0.83 | 0.79 | 0.77 | 0.76 |
102 | 11 | 1 | 11 | 25 | 0.5 | -3 | 2 | Symm | 3 | 0 | 1 | Symm | 0.39 | 0.51 | 0.59 | 0.62 | 0.59 |
103 | 27 | 0.8 | -4 | 77 | 0.1 | 22 | 1 | R-skew | 6 | -1 | 0 | R-skew | 0.83 | 0.82 | 0.73 | 0.78 | 0.77 |
104 | -6 | 1 | -6 | 3 | 0.99 | -27 | 0 | - | 1 | 0 | 0 | - | 0.85 | 0.95 | 0.98 | 0.97 | 0.98 |
105 | 30 | 1 | 30 | 90 | 0.01 | 36 | 0 | - | 1 | 0 | 0 | - | 0.9 | 0.97 | 1 | 1 | 1 |
106 | 2 | 1 | 2 | 34 | 0.05 | -5 | 2 | Symm | 5 | 0 | 0 | Symm | 0.2 | 0.14 | 0.15 | 0.15 | 0.12 |
107 | 25 | 1 | 25 | 65 | 0.25 | 9 | 2 | Symm | 5 | 0 | 0 | Symm | 0.39 | 0.39 | 0.4 | 0.37 | 0.32 |
108 | 16 | 1 | 16 | 91 | 0.2 | -11 | 0 | - | 1 | 0 | 0 | - | 0.27 | 0.17 | 0.23 | 0.19 | 0.18 |
109 | 11 | 1 | 11 | 26 | 0.5 | -9 | 0 | - | 0 | 0 | 0 | - | 0.33 | 0.41 | 0.47 | 0.38 | 0.4 |
110 | 12 | 1 | 12 | 29 | 0.8 | -35 | 1 | L-skew | 2 | 0 | 0 | R-skew | 0.56 | 0.72 | 0.71 | 0.7 | 0.77 |
111 | 28 | 1 | 28 | 47 | 0.6 | -13 | 0 | - | 1 | 0 | 0 | - | 0.25 | 0.41 | 0.41 | 0.4 | 0.39 |
112 | -7 | 1 | -7 | 28 | 0.2 | -18 | 2 | Symm | 7 | 0 | 0 | Symm | 0.51 | 0.36 | 0.31 | 0.29 | 0.26 |
113 | 9 | 0.95 | 0 | 37 | 0.25 | -3 | 1 | R-skew | 6 | 0 | 0 | R-skew | 0.35 | 0.37 | 0.37 | 0.38 | 0.37 |
114 | 72 | 0.01 | -2 | 112 | 0.25 | -33 | 0 | - | 1 | -1 | 0 | - | 0.44 | 0.45 | 0.4 | 0.42 | 0.32 |
115 | 50 | 0.4 | 5 | 20 | 0.8 | -17 | 2 | Symm | 7 | 0 | 0 | Symm | 0.17 | 0.19 | 0.23 | 0.2 | 0.2 |
116 | 2 | 1 | 2 | 45 | 0.05 | 3 | 2 | Symm | 5 | 0 | 0 | Symm | 0.95 | 0.99 | 1 | 1 | 1 |
117 | -6 | 1 | -6 | 7 | 0.5 | -30 | 0 | - | 1 | 0 | 0 | - | 0.33 | 0.39 | 0.36 | 0.35 | 0.34 |
118 | 26 | 1 | 26 | 46 | 0.5 | 10 | 1 | L-skew | 6 | 0 | 0 | R-skew | 0.47 | 0.56 | 0.62 | 0.59 | 0.57 |
119 | 19 | 0.4 | 12 | 100 | 0.25 | -12 | 1 | R-skew | 2 | 0 | 0 | R-skew | 0.33 | 0.32 | 0.34 | 0.34 | 0.35 |
120 | -9 | 0.95 | -26 | -1 | 0.1 | -11 | 0 | - | 1 | 0 | 0 | - | 0.57 | 0.41 | 0.43 | 0.46 | 0.42 |
121 | -8 | 1 | -8 | 21 | 0.01 | 0 | 2 | Symm | 3 | 0 | 0 | Symm | 0.79 | 0.95 | 0.99 | 1 | 0.99 |
122 | 68 | 0.05 | -14 | -11 | 0.9 | -36 | 0 | - | 1 | 0 | 0 | - | 0.36 | 0.39 | 0.42 | 0.46 | 0.4 |
123 | 28 | 0.75 | -13 | 57 | 0.1 | 16 | 0 | - | 1 | 0 | 0 | - | 0.74 | 0.64 | 0.66 | 0.7 | 0.63 |
124 | 15 | 0.95 | 7 | 42 | 0.01 | 19 | 0 | - | 1 | 0 | 0 | - | 0.85 | 0.96 | 0.97 | 0.97 | 0.98 |
125 | 28 | 1 | 28 | 41 | 0.4 | 12 | 0 | - | 1 | 0 | 0 | - | 0.29 | 0.36 | 0.33 | 0.33 | 0.36 |
126 | -8 | 1 | -8 | 80 | 0.2 | -18 | 2 | Symm | 7 | 0 | 0 | Symm | 0.53 | 0.52 | 0.51 | 0.49 | 0.52 |
127 | 4 | 1 | 4 | 29 | 0.6 | -40 | 0 | - | 1 | 0 | 1 | - | 0.26 | 0.33 | 0.44 | 0.46 | 0.44 |
128 | -3 | 1 | -3 | 32 | 0.4 | -16 | 0 | - | 1 | 0 | 0 | - | 0.64 | 0.57 | 0.56 | 0.57 | 0.56 |
129 | -2 | 1 | -2 | -2 | 1 | -2 | 2 | Symm | 9 | 0 | 0 | Symm | 0.46 | 0.53 | 0.51 | 0.48 | 0.53 |
130 | 72 | 0.4 | -41 | 16 | 0.01 | 1 | 0 | - | 1 | 0 | 0 | - | 0.61 | 0.6 | 0.56 | 0.54 | 0.54 |
131 | 18 | 1 | 18 | 45 | 0.01 | 11 | 0 | - | 1 | 0 | 0 | - | 0.19 | 0.09 | 0.08 | 0.08 | 0.06 |
132 | 11 | 1 | 11 | 20 | 0.99 | 4 | 2 | Symm | 7 | 0 | 0 | Symm | 0.81 | 0.94 | 0.97 | 0.97 | 0.98 |
133 | 3 | 1 | 3 | 8 | 0.99 | -17 | 2 | Symm | 9 | 0 | 0 | Symm | 0.71 | 0.91 | 0.92 | 0.92 | 0.94 |
134 | 27 | 0.05 | 24 | 31 | 0.5 | 10 | 2 | Symm | 3 | 0 | 0 | Symm | 0.34 | 0.34 | 0.38 | 0.38 | 0.37 |
135 | 6 | 1 | 6 | 8 | 0.5 | -1 | 0 | - | 1 | 0 | 0 | - | 0.25 | 0.32 | 0.31 | 0.29 | 0.29 |
136 | 4 | 1 | 4 | 25 | 0.01 | -5 | 0 | - | 1 | 0 | 0 | - | 0.16 | 0.07 | 0.07 | 0.05 | 0.05 |
137 | 3 | 1 | 3 | 4 | 0.4 | 3 | 2 | Symm | 5 | 0 | 1 | Symm | 0.73 | 0.86 | 0.9 | 0.9 | 0.9 |
138 | 23 | 1 | 23 | 21 | 0.8 | 16 | 0 | - | 1 | 0 | 0 | - | 0.13 | 0.07 | 0.01 | 0.02 | 0.02 |
139 | 14 | 1 | 14 | 35 | 0.6 | -9 | 2 | Symm | 7 | 0 | 0 | Symm | 0.48 | 0.67 | 0.7 | 0.64 | 0.65 |
140 | -2 | 1 | -2 | 9 | 0.25 | 8 | 0 | - | 1 | 0 | 0 | - | 0.91 | 0.98 | 0.98 | 0.99 | 0.98 |
141 | 28 | 0.8 | -26 | 22 | 0.75 | 2 | 0 | - | 1 | 0 | 0 | - | 0.77 | 0.7 | 0.62 | 0.6 | 0.62 |
142 | 23 | 1 | 23 | 29 | 0.8 | -8 | 0 | - | 1 | 0 | 0 | - | 0.3 | 0.44 | 0.43 | 0.51 | 0.54 |
143 | 67 | 0.5 | -39 | 93 | 0.25 | -15 | 0 | - | 1 | 0 | 0 | - | 0.53 | 0.58 | 0.54 | 0.6 | 0.63 |
144 | 16 | 0.8 | 12 | 15 | 1 | 15 | 2 | Symm | 9 | 0 | 0 | Symm | 0.42 | 0.5 | 0.44 | 0.42 | 0.42 |
145 | 17 | 0.5 | -27 | 3 | 0.75 | -35 | 2 | Symm | 7 | 0 | 0 | Symm | 0.42 | 0.43 | 0.42 | 0.34 | 0.34 |
146 | 45 | 0.2 | 3 | 75 | 0.05 | 13 | 2 | Symm | 5 | 0 | 0 | Symm | 0.79 | 0.82 | 0.84 | 0.87 | 0.84 |
147 | 29 | 1 | 29 | 36 | 0.1 | 32 | 2 | Symm | 7 | 0 | 0 | Symm | 0.88 | 0.96 | 0.99 | 0.98 | 0.97 |
148 | 65 | 0.01 | 1 | 12 | 0.01 | 3 | 0 | - | 1 | -1 | 1 | - | 0.73 | 0.81 | 0.82 | 0.84 | 0.85 |
149 | 12 | 1 | 12 | 31 | 0.1 | 12 | 2 | Symm | 3 | 0 | 0 | Symm | 0.86 | 0.9 | 0.92 | 0.91 | 0.94 |
150 | 16 | 1 | 16 | 24 | 0.05 | 12 | 1 | L-skew | 3 | 0 | 0 | R-skew | 0.35 | 0.25 | 0.22 | 0.19 | 0.17 |