获得领域中单结果风险决策齐当别理论的数学建模 | |
Alternative Title | Mathematical Modeling of Equate-to一Differentiate Theorv for Single-Outcome Riskv Choices in the Gain Domain |
李云箫 | |
Contributor | 李纾 |
2021-06 | |
Abstract | 在单结果风险决策中，前人发现了违背独立性公理的共同比率效应，和违背传递性公理的非传递性现象。预期理论允许且可以解释共同比率效应，但不允许且不能解释非传递性现象。比例差异模型允许且可以解释非传递性现象，但不允许且不能解释共同比率效应。齐当别理论是一个借助弱占优原则达成决策的理论。在单结果风险决策中，齐当别理论认为人们会比较两个选项的结果主观差异(△outcome)和概率主观差异(△probability），如果△outcome/△probability更大，则人们会将较小的△probability/△outcom。视作没有差异(齐同)，即视两个选项构成弱占优的关系。遵循弱占优原则，人们会选择结果更大/概率更高的选项(辨别)。 虽然共同比率效应和非传递性现象均可以被齐当别理论所解释，但该理论目前还是一个定性的决策理论。因此，本研究旨在1)为齐当别理论建立一个定量的数学模型，2)将建模后的齐当别理论与已建立定量数学模型的预期理论和比例差异模型相比较以验优劣。为了达到这个目的，我们设计了三个研究。 在研究1中，我们将非参数诱导法与直观模拟天平相结合，使用标准结果序列和标准概率序列，确定每一名被试在获得领域下齐当别理论的效用函数与主观概率函数的形状。该实验包括序列递增和序列递减两个条件，采用被试内设计。结果表明，1)分别或同时考虑两个条件，凹效用函数的被试数量比例均显著大于50%，该结果支持边际效用递减的假设;2)在序列递减时，反S形主观概率函数的被试数量比例大于50%，而在序列递增或同时考虑两个条件时，该比例与50%无显著差异，该结果并没有强支持反S形主观概率函数的假设，而展现出较大的个体差异，主观概率函数表现为反S形函数的被试最多，但分别有32%的被试和25%的被试的主观概率函数至少在一种条件下不确定或表现为凹函数。 在研究2中，我们提出了齐当别理论的定量数学表达:1)基于被试边际效用递减的结果，我们选用Kirby (2011)提出的对数函数作为齐当别理论的效用函数，以描述人们对金钱的主观感知;2)基于被试的主观概率函数可能为反S形函数或凹函数的结果，我们选用Prelec (1998)提出的双参数指数函数作为齐当别理论的主观概率函数，以描述人们对客观概率的主观感知;3)参考前人研究，我们构建出齐当别理论的属性差异函数，以描述人们对属性间(结果属性vs概率属性)差异的知觉。 在研究3中，我们收集了被试在20对单结果风险决策选项上的决策数据，随机选取16对选项对应的全部被试的决策结果作为训练集，用于拟合齐当别理论、比例差异模型和预期理论，随后使用三个模型的拟合结果分别预测被试在其余4对选项中的决策(测试集)。结果表明，在三个相互竞争模型中，齐当别理论在训练集上的拟合优度最大且样本外可预测性最高，对测试集的数据提供了最好的预测。 总之，本研究提出了齐当别理论的改良版本，将定性的齐当别理论发展为可应用于获得领域中单结果风险决策的定量的数学模型，有望为该理论今后在损失领域中单结果风险决策的建模，以及在跨期决策和空间决策的数学建模奠定基础。 |
Other Abstract | In single-outcome risk choices, the common patio effect, which violates the independence axiom, and intransitivity, which violates the transitivity axiom, have been reported in the literature. Prospect theory can account for the common ratio effect but not for intransitivity, whereas the proportional difference model can account for intransitivity but not for the common ratio effect. The equate-to-differentiate theory (ETD) is proposed so that weak-dominance principle can be made applicable in binary choice. In single-outcome risk choices, ETD suggests that people tend to compare the subjective difference in outcomes (△outcome) and the subjective difference in probabilities (△probability) between the two options, and if △outcome/△probability is greater, then people will treat the smaller △probability/△outcome as if there is no difference (equate). In other words, the two options are treated as if they have a weak-dominance relationship. Following the weak-dominance principle, people are likely to choose the option with greater outcome or probability (differentiate) than other options. Although both common ratio effect and intransitivity can be explained by ETD, the theory is, thus far, a qualitative theory of decision making. Therefore, the aim of the current study is two-fold: 1)to develop a quantitative mathematical model for ETD and 2) to carry out model comparison among the newly modeled ETD and two quantitative mathematical models, namely, prospect theory and proportional difference model. Three studies were designed to achieve this goal. In Study 1，we use the parameter-free elicitation and visual analogue scale to determine the shape of each subject's utility function and subjective probability function of ETD in the gain domain using a standard outcome sequence and a standard probability sequence. A within-subj ects, two-condition (increasing and decreasing sequences) experimental design was developed in this study. According to the results: 1)the proportion of subjects with concave utility functions was significantly greater than 50%, either when evaluated simultaneously in both conditions or separately in each condition, thus supporting the hypothesis of diminishing marginal utility, and 2) the proportion of subjects with the inverse S-shaped subjective probability function was significantly greater than 50% in decreasing sequences, whereas this proportion did not differ from 50% in decreasing sequences or in both conditions, thus indicating a large individual variation in subjective probability functions, rather strongly supporting the场pothesis of S-shaped subjective probability function, with the largest number of subjects exhibiting inverse S-shaped functions, but the subjective probability functions of 32% of the subjects and 25% of the subjects, respectively, were uncertain or concave in at least one condition. In Study 2, we proposed a quantitative mathematical representation of ETD. First based on our finding, which suggested a diminishing marginal utility, we chose the logarithmic function proposed by Kirby (2011)as the utility function of ETD to describe people's subjective perception of money. Second, also based on our finding, which suggested that the subjective function is S-shaped or concave, we chose the two-parameter exponential function proposed by Prelec (1998) as the subjective probability function of ETD to describe people's subjective perception of objective probability. Third, taking account of previous research, we proposed an attribute difference function of ETD to describe people's perceptions of the differences between attributes (outcome vs. probability). In Study 3, we collected data of individuals' decisions on 20 pairs of single-outcome risk choices, and randomly selected 16 pairs as the training sets for fitting ETD, the proportional difference model, and prospect theory. Then, we used the fitting results of the three models to predict individuals' decision outcomes in each of the remaining four pairs (test set). Results showed that, of the three competing models, ETD provided the largest goodness-of-fit and the highest out-of-sample predictability of the data from training set. Furthermore, ETD provided the best account of the data from the test set. In summary, this study developed a refined version of ETD, proposing a mathematical representation of ETD for single-outcome risk choices in the gain domain. The findings of this work could help lay a foundation for further modeling for single-outcome risk choices in the loss domain and, hopefully, for modelling for intertemporal choices and spatial choices in the future. |
Keyword | 风险决策 齐当别理论 非参数诱导法 模型比较 |
Subtype | 硕士 |
Language | 中文 |
Degree Name | 理学硕士 |
Degree Discipline | 应用心理 |
Degree Grantor | 中国科学院心理研究所 |
Place of Conferral | 中国科学院心理研究所 |
Document Type | 学位论文 |
Identifier | http://ir.psych.ac.cn/handle/311026/39564 |
Collection | 社会与工程心理学研究室 |
Recommended Citation GB/T 7714 | 李云箫. 获得领域中单结果风险决策齐当别理论的数学建模[D]. 中国科学院心理研究所. 中国科学院心理研究所,2021. |
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