当前位置: X-MOL 学术Theoretical Economics › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the falsifiability and learnability of decision theories
Theoretical Economics ( IF 1.671 ) Pub Date : 2020-01-01 , DOI: 10.3982/te3438
Pathikrit Basu 1 , Federico Echenique 1
Affiliation  

We study the degree of falsifiability of theories of choice. A theory is easy to falsify if relatively small datasets are enough to guarantee that the theory can be falsified: the VC dimension of a theory is the largest sample size for which the theory is ``never falsifiable.'' VC dimension is motivated strategically. We consider a model with a strategic proponent of a theory, and a skeptical consumer, or user, of theories. The former presents experimental evidence in favor of the theory, and the latter may doubt whether the experiment could ever have falsified the theory. We focus on decision-making under uncertainty, considering the central models of Expected Utility, Choquet Expected Utility and Max-min Expected Utility models. We show that Expected Utility has VC dimension that grows linearly with the number of states while that of Choquet Expected Utility grows exponentially. The Max-min Expected Utility model has infinite VC dimension when there are at least three states of the world. In consequence, Expected Utility is easily falsified, while the more flexible Choquet and Max-min Expected Utility are hard to falsify. Finally, as VC dimension and statistical estimation are related, we study the implications of our results for machine learning approaches to preference recovery.

中文翻译:

论决策理论的可证伪性和可学习性

我们研究选择理论的可证伪程度。如果相对较小的数据集足以保证理论可以被证伪,则理论很容易被证伪:理论的 VC 维是理论“永远不可证伪”的最大样本量。VC 维是战略性的。我们考虑一个模型,其中有一个理论的战略支持者和一个对理论持怀疑态度的消费者或用户。前者提供了支持该理论的实验证据,而后者可能会怀疑该实验是否曾证伪过该理论。我们关注不确定性下的决策,考虑了预期效用、Choquet 预期效用和 Max-min 预期效用模型的中心模型。我们表明,预期效用的 VC 维度随状态数线性增长,而 Choquet 预期效用的 VC 维度呈指数增长。当世界至少存在三种状态时,最大-最小期望效用模型具有无限的 VC 维数。因此,Expected Utility 很容易被证伪,而更灵活的 Choquet 和 Max-min Expected Utility 则很难被证伪。最后,由于 VC 维度和统计估计是相关的,我们研究了我们的结果对机器学习方法对偏好恢复的影响。
更新日期:2020-01-01
down
wechat
bug