Acta Psychologica Sinica ›› 2022, Vol. 54 ›› Issue (12): 1517-1531.doi: 10.3724/SP.J.1041.2022.01517
• Reports of Empirical Studies • Previous Articles Next Articles
LIU Hong-Zhi3, LI Xingshan1,2, LI Shu1,2,4, RAO Li-Lin1,2()
Received:
2022-01-22
Published:
2022-12-20
Online:
2022-09-23
Contact:
RAO Li-Lin
E-mail:raoll@psych.ac.cn
Supported by:
LIU Hong-Zhi, LI Xingshan, LI Shu, RAO Li-Lin. (2022). When expectation-maximization-based theories work or do not work: An eye-tracking study of the discrepancy between everyone and every one. Acta Psychologica Sinica, 54(12), 1517-1531.
Model | Decision rule |
---|---|
Expected value (EV) theory | Calculate the sum of all weighted possible outcomes using the formula Σ pi · xi. Choose the gamble with the highest weighted sum. |
Expected utility (EU) theory | Calculate the sum of all weighted outcomes using the following formula: Σ pi · u(xi). Choose the gamble with the highest weighted sum. We assumed the utility function u(xi) = log(xi) in this study (Su et al., |
Cumulative prospect theory (CPT) | Calculate the sum of all weighted outcomes using the following formula: Σ π(pi) · v(xi), π(pi) = piγ/[ piγ + (1 - pi)γ]1/γ, v(xi) = xiα. Choose the gamble with the highest weighted sum. We estimated the values of parameters in individual level. |
Equate-to-differentiate (ETD) model | Choose the gamble with more attractive gain on the dimension (best or worst payoff) with the greatest intradimensional utility difference. We assumed the utility function u(xi) = log(xi) in this study (Su et al., |
Maximax heuristic (MH) | Choose the gamble with the highest monetary payoff. |
Tallying heuristic (TH) | Give a tally mark to the gamble with (a) the higher minimum gain, (b) the higher maximum gain, (c) the lower probability of the minimum gain, and (d) the higher probability of the maximum gain. Select the gamble with the higher number of tally marks. |
Table 1 Decision rules of 6 models tested in predicting choice data
Model | Decision rule |
---|---|
Expected value (EV) theory | Calculate the sum of all weighted possible outcomes using the formula Σ pi · xi. Choose the gamble with the highest weighted sum. |
Expected utility (EU) theory | Calculate the sum of all weighted outcomes using the following formula: Σ pi · u(xi). Choose the gamble with the highest weighted sum. We assumed the utility function u(xi) = log(xi) in this study (Su et al., |
Cumulative prospect theory (CPT) | Calculate the sum of all weighted outcomes using the following formula: Σ π(pi) · v(xi), π(pi) = piγ/[ piγ + (1 - pi)γ]1/γ, v(xi) = xiα. Choose the gamble with the highest weighted sum. We estimated the values of parameters in individual level. |
Equate-to-differentiate (ETD) model | Choose the gamble with more attractive gain on the dimension (best or worst payoff) with the greatest intradimensional utility difference. We assumed the utility function u(xi) = log(xi) in this study (Su et al., |
Maximax heuristic (MH) | Choose the gamble with the highest monetary payoff. |
Tallying heuristic (TH) | Give a tally mark to the gamble with (a) the higher minimum gain, (b) the higher maximum gain, (c) the lower probability of the minimum gain, and (d) the higher probability of the maximum gain. Select the gamble with the higher number of tally marks. |
Figure 2. Percentage of choices that were correctly predicted by expectation theories and heuristic/non-expectation theories in (a) the D-everyone task, (b) the D-multiple task, and (3) the D-single task. Error bars represent standard errors of the means.
Figure 3. Similarity scores for the intra-task and the inter-task in the D-everyone, D-multiple, and D-single tasks. Error bars represent standard errors of the means. ***p < 0.001,**p < 0.01, *p < 0.05.
Variable | df | F | p | η2p | Variable | df | F | p | η2p |
---|---|---|---|---|---|---|---|---|---|
PTIS | SMI | ||||||||
Task | 2, 94 | 5.02 | 0.008 | 0.10 | Task | 2, 94 | 8.59 | < 0.001 | 0.16 |
ED | 2, 94 | 0.19 | 0.827 | 0.00 | ED | 2, 94 | 0.72 | 0.487 | 0.02 |
OD | 2, 94 | 3.68 | 0.029 | 0.07 | OD | 2, 94 | 0.32 | 0.725 | 0.01 |
Task × ED | 4, 188 | 1.03 | 0.396 | 0.02 | Task × ED | 4, 188 | 1.60 | 0.177 | 0.03 |
Task × OD | 4, 188 | 2.96 | 0.021 | 0.06 | Task × OD | 4, 188 | 0.16 | 0.961 | 0.00 |
ED × OD | 4, 188 | 0.57 | 0.686 | 0.01 | ED × OD | 4, 188 | 6.84 | < 0.001 | 0.13 |
Task × ED × OD | 8, 376 | 0.93 | 0.488 | 0.02 | Task × ED × OD | 8, 376 | 1.20 | 0.298 | 0.03 |
MFD | PSTB | ||||||||
Task | 2, 94 | 10.94 | < 0.001 | 0.19 | Task | 2, 94 | 9.03 | < 0.001 | 0.16 |
ED | 2, 94 | 22.75 | < 0.001 | 0.33 | ED | 2, 94 | 1.49 | 0.230 | 0.03 |
OD | 2, 94 | 2.93 | 0.058 | 0.06 | OD | 2, 94 | 5.14 | 0.008 | 0.10 |
Task × ED | 4, 188 | 5.78 | < 0.001 | 0.11 | Task × ED | 4, 188 | 0.96 | 0.433 | 0.02 |
Task × OD | 4, 188 | 1.22 | 0.304 | 0.03 | Task × OD | 4, 188 | 0.86 | 0.491 | 0.02 |
ED × OD | 4, 188 | 3.65 | 0.007 | 0.07 | ED × OD | 4, 188 | 0.33 | 0.860 | 0.01 |
Task × ED × OD | 8, 376 | 1.79 | 0.079 | 0.04 | Task × ED × OD | 8, 376 | 1.30 | 0.244 | 0.03 |
Table 2 Summary of repeated measures ANOVA on PTIS, MFD, SMI, and PSTB across task, EV difference, and outcome difference
Variable | df | F | p | η2p | Variable | df | F | p | η2p |
---|---|---|---|---|---|---|---|---|---|
PTIS | SMI | ||||||||
Task | 2, 94 | 5.02 | 0.008 | 0.10 | Task | 2, 94 | 8.59 | < 0.001 | 0.16 |
ED | 2, 94 | 0.19 | 0.827 | 0.00 | ED | 2, 94 | 0.72 | 0.487 | 0.02 |
OD | 2, 94 | 3.68 | 0.029 | 0.07 | OD | 2, 94 | 0.32 | 0.725 | 0.01 |
Task × ED | 4, 188 | 1.03 | 0.396 | 0.02 | Task × ED | 4, 188 | 1.60 | 0.177 | 0.03 |
Task × OD | 4, 188 | 2.96 | 0.021 | 0.06 | Task × OD | 4, 188 | 0.16 | 0.961 | 0.00 |
ED × OD | 4, 188 | 0.57 | 0.686 | 0.01 | ED × OD | 4, 188 | 6.84 | < 0.001 | 0.13 |
Task × ED × OD | 8, 376 | 0.93 | 0.488 | 0.02 | Task × ED × OD | 8, 376 | 1.20 | 0.298 | 0.03 |
MFD | PSTB | ||||||||
Task | 2, 94 | 10.94 | < 0.001 | 0.19 | Task | 2, 94 | 9.03 | < 0.001 | 0.16 |
ED | 2, 94 | 22.75 | < 0.001 | 0.33 | ED | 2, 94 | 1.49 | 0.230 | 0.03 |
OD | 2, 94 | 2.93 | 0.058 | 0.06 | OD | 2, 94 | 5.14 | 0.008 | 0.10 |
Task × ED | 4, 188 | 5.78 | < 0.001 | 0.11 | Task × ED | 4, 188 | 0.96 | 0.433 | 0.02 |
Task × OD | 4, 188 | 1.22 | 0.304 | 0.03 | Task × OD | 4, 188 | 0.86 | 0.491 | 0.02 |
ED × OD | 4, 188 | 3.65 | 0.007 | 0.07 | ED × OD | 4, 188 | 0.33 | 0.860 | 0.01 |
Task × ED × OD | 8, 376 | 1.79 | 0.079 | 0.04 | Task × ED × OD | 8, 376 | 1.30 | 0.244 | 0.03 |
Figure 4. Results of eye-tracking measures. (a) The percentage of total information searched (PTIS). (b) The mean fixation duration (MFD). (c) The alternative-based versus dimension-based search measure index (SMI). (d) The proportion of the saccades between the two best outcomes (PSTB). Error bars represent standard errors of the means. ***p < 0.001, **p < 0.01, *p < 0.05.
Figure 5. Results of mediation analysis. (a) Mediating effect of eye-tracking measures on the relationship between task (D-single task vs. D-everyone task) and the percentage of the EV-consistent choice. (b) Mediating effect of eye-tracking measures on the relationship between task (D-single task vs. D-multiple task) and EV-consistent choice. ***p < 0.001.
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