Table 2.
Illustrative motivating example. The 10 gamble pairs are the Cash II stimulus set of Regenwetter et al. (2010, 2011a). KT-V4 denotes a specific theoretical prediction made by Kahneman and Tversky's Cumulative Prospect Theory. HDM is an illustrative hypothetical decision maker, and DM1 and DM13 are Participants 1 and 13 in Regenwetter et al. (2010, 2011a). The right three columns show the frequencies, out of 20 repetitions, and corresponding percentages, that each decision maker chose the cash lottery coded as Gamble 1. Frequencies where the modal choice is consistent with KT-V4 are marked in typewriter style, cases where the modal choice is inconsistent with KT-V4 are underlined, unmarked choice frequencies are exactly at the 50% boundary. Significant violations (α = 0.05) are marked in bold font.
| Pair | Monetary gamble coded as Gamble 1 | Monetary gamble coded as Gamble 0 | KT-V4 Preferred | HDM # choices | DM1 # choices | DM13 # choices | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Chance | Gain | Chance | Gain | Gamble | Gamble 1 | Gamble 1 | Gamble 1 | ||||
| 1 | A: 28% | $31.43 | B: 32% | $27.50 | 1 | 18 | 90% | 17 | 85% | 16 | 80% |
| 2 ◊ | A: 28% | $31.43 | C: 36% | $24.44 | 1 | 19 | 95% | 13 | 65% | 9 | 45% |
| 3 ⊕ | A: 28% | $31.43 | D: 40% | $22 | 0 | 1 | 5% | 5 | 25% | 12 | 60% |
| 4 | A: 28% | $31.43 | E: 44% | $20 | 0 | 0 | 0% | 4 | 20% | 7 | 35% |
| 5 | B: 32% | $27.50 | C: 36% | $24.44 | 1 | 20 | 100% | 17 | 85% | 10 | 50% |
| 6 | B: 32% | $27.50 | D: 40% | $22 | 0 | 3 | 15% | 8 | 40% | 8 | 40% |
| 7 | B: 32% | $27.50 | E: 44% | $20 | 0 | 0 | 0% | 3 | 15% | 9 | 45% |
| 8 ◁ | C: 36% | $24.44 | D: 40% | $22 | 0 | 2 | 10% | 15 | 75% | 12 | 60% |
| 9 | C: 36% | $24.44 | E: 44% | $20 | 0 | 1 | 5% | 9 | 45% | 11 | 55% |
| 10 | D: 40% | $22 | E: 44% | $20 | 0 | 0 | 0% | 10 | 50% | 10 | 50% |
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| Descriptive Analysis: | |||||||||||
| Total number of choices matching KT-V4 | 190 | 95% | 133 | 67% | 106 | 53% | |||||
| Number of modal choices matching KT-V4 | 10 | 8 (or 9) | 4 (or 6) | ||||||||
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| Semi-quantitative Analysis (α = .05): | |||||||||||
| Number of signif. 2-sided Binomial tests for/against KT-V4 | 10 / 0 | 5 / 1 | 1 / 0 | ||||||||
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| QTest (p-values) for KT-V4: | |||||||||||
| Modal Choice (Permit up to 50% error rate in each pair): | 1 | 0.03 | .55 | ||||||||
| 0.75-supermajority (Permit up to 25% error rate in each pair): | 1 | < 0.00001 | < 0.00001 | ||||||||
| 0.50-city-block .50 (Sum of 10 error rates may be at most .50): | 1 | < 0.00001 | < 0.00001 | ||||||||
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| “Kahneman-Tversky” (12 possible preference states): | 0.045 | 0.0002 | 0.36 | ||||||||
| “Goldstein-Einhorn” (43 possible preference states): | 0.25 | 0.01 | 0.20 | ||||||||