基于期望值最大化的理论何时失效：风险决策中为自己-为所有人决策差异的眼动研究

doi:10.3724/SP.J.1041.2022.01517

摘要/Abstract

摘要：

主流的风险决策理论专家发展了一系列基于期望值最大化(expectation-maximization)的理论, 以期捕获所有人的风险决策行为。然而大量证据表明, 这些基于期望值最大化的理论并不能如同描述性理论那样理想地描述单一个体的决策行为。本研究采用眼动追踪技术, 系统考察了个体在为所有人决策与为自己决策时的风险决策行为及信息加工过程的差异。本研究发现, 基于期望值最大化的理论可捕获为所有人决策或为自己多次决策时的情况, 却不能很好捕获个体为自己进行单次决策时的情况。本研究结果有助于理解基于期望值最大化的理论与启发式/非基于期望值最大化的理论的边界, 为风险决策理论的划分和发展提供实证参考。

关键词: 风险决策, 为所有人决策, 期望值最大化, 为自己-为所有人决策差异, 眼动追踪技术

Abstract:

Mainstream theorists in risky decision-making have developed various expectation-maximization-based theories with the ambitious goal of capturing everyone’s choices. However, ample evidence has revealed that these theories could not capture every individual’s (“every one’s”) actual risky choice as descriptive theories. Substantial research has demonstrated that people do not follow the logical process suggested by expectation-maximization-based theories when making risky choices but rather rely on simplifying heuristics. From our perspective, the possible reason why mainstream decision theorists did not abandon the framework of expectation is that these theorists never doubted the validity of the expectation rule as a descriptive rule in describing decision-making under risk. We believe that expectation-maximization-based theories may capture risky choices when individuals make decisions for everyone. However, whether these theories could capture risky choices when individuals make decisions for themselves cannot be taken for granted. We thus used an eye-tracking technique to explore whether a theory for everyone would work well for every one.

A total of 52 college students participated in the experiment. Three risky choice tasks were conducted in the present study: a D-everyone task, a D-multiple task, and a D-single task. In the D-everyone task, participants were asked to choose the more optimal option out of two options under the assumption that their selection would be the final decision for everyone who was facing the same choice—that is, everyone would be subject to the same choice but could receive different outcomes. In the D-multiple task, participants were asked to choose between the two options under the assumption that their selection would be applied a total of 100 times. In the D-single task, participants were asked to choose between the two options under the assumption that their selection would be applied only once to themselves. The participants’ eye movements were recorded while they performed the tasks.

Behavioral results revealed that, compared with the D-single task, participants selected more choices correctly predicted by EV and EU theories, and took a longer time to make a decision in the D-everyone and D-multiple tasks. Furthermore, eye movement measurements revealed the following. (1) The scanpath patterns of the D-everyone task and D-multiple task were similar but different from those of the D-single task. (2) The depth of information acquisition and the level of complexity of information processing in the D-everyone task and D-multiple task was higher than that in the D-single task. (3) The direction of information search in the D-everyone task and D-multiple task was more alternative-based than that in the D-single task. (4) The eye-tracking measures mediated the relationship between the task and the EV-consistent choice. In summary, behavioral and eye movement results supported our hypotheses that participants were likely to follow an expectation strategy in the D-everyone and D-multiple tasks, whereas they were likely to follow a heuristic/non- expectation strategy in the D-single task.

We found that expectation-maximization-based theories could capture the choice of an individual when making decisions for everyone and for self in a multiple-play condition but could not capture the choice of an individual when making decisions for self in a single-play condition. The evidence for the discrepancy between everyone and every one, which was first reported in our study, implied that the possible reason why expectation-maximization-based theories do not work is that a default compatibility between the full set (everyone) and the subset (every one) does not exist. Our findings contribute to an improved understanding of the boundaries of expectation-maximization-based theories and those of heuristic/non-expectation models. Our findings may also shed light on the general issue of the classification of risky decision-making theories.

Key words: risky choice, decision for everyone, expectation-maximization, discrepancy between everyone and every one, eye-tracking

中图分类号:

B849: C91

刘洪志, 李兴珊, 李纾, 饶俪琳. (2022). 基于期望值最大化的理论何时失效：风险决策中为自己-为所有人决策差异的眼动研究. 心理学报, 54(12), 1517-1531.

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.

图/表 8

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模型	决策规则
Expected value (EV) theory	基于公式Σ p_i · x_i计算所有可能结果的加权值的总和, 并选择加权求和总值最高的选项。
Expected utility (EU) theory	基于公式Σ p_i · u (x_i)计算加权结果的总和, 并选择加权求和总值最高的选项。本研究采用对数效用函数: u (x_i) = log (x_i) (Su et al., 2013)。
Cumulative prospect theory (CPT)	基于公式Σ π(p_i) · v (x_i)计算加权结果的总和, 并选择加权求和总值最高的选项。其中π(p_i) = p_i^γ/[ p_i^γ + (1 - p_i)^γ]^1/^γ, v (x_i) = x_i^α。本研究采用正确率最大化的方法在个体水平估计参数值, 即对于每一个体, 估计出CPT模型对该个体预测正确率最高的一组参数值。
Equate-to-differentiate (ETD) model	根据在维度内效用差异最大的维度(最好可能结果维度或最差可能结果维度)进行决策, 选择在此维度上获益更大的选项。本研究采用对数效用函数的形式: u (x_i) = log (x_i) (Su et al., 2013)。
Maximax heuristic (MH)	选择在最好可能结果维度上获益更大的选项。
Tallying heuristic (TH)	选项满足以下条件则计数: (a) 在最差结果维度获益较高, (b) 在最好结果维度获益较高, (c) 最差结果对应的概率较低, (d) 最好结果对应的概率较高。最终选择计数标记较高的选项。

模型	决策规则
Expected value (EV) theory	基于公式Σ p_i · x_i计算所有可能结果的加权值的总和, 并选择加权求和总值最高的选项。
Expected utility (EU) theory	基于公式Σ p_i · u (x_i)计算加权结果的总和, 并选择加权求和总值最高的选项。本研究采用对数效用函数: u (x_i) = log (x_i) (Su et al., 2013)。
Cumulative prospect theory (CPT)	基于公式Σ π(p_i) · v (x_i)计算加权结果的总和, 并选择加权求和总值最高的选项。其中π(p_i) = p_i^γ/[ p_i^γ + (1 - p_i)^γ]^1/^γ, v (x_i) = x_i^α。本研究采用正确率最大化的方法在个体水平估计参数值, 即对于每一个体, 估计出CPT模型对该个体预测正确率最高的一组参数值。
Equate-to-differentiate (ETD) model	根据在维度内效用差异最大的维度(最好可能结果维度或最差可能结果维度)进行决策, 选择在此维度上获益更大的选项。本研究采用对数效用函数的形式: u (x_i) = log (x_i) (Su et al., 2013)。
Maximax heuristic (MH)	选择在最好可能结果维度上获益更大的选项。
Tallying heuristic (TH)	选项满足以下条件则计数: (a) 在最差结果维度获益较高, (b) 在最好结果维度获益较高, (c) 最差结果对应的概率较低, (d) 最好结果对应的概率较高。最终选择计数标记较高的选项。

变量	df	F	p	η²_p	变量	df	F	p	η²_p
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

变量	df	F	p	η²_p	变量	df	F	p	η²_p
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