Collaborative Research: Quantum Decision Theory

合作研究：量子决策理论

• 批准号: 0817965
• 负责人: Jerome Busemeyer
• 金额: $ 21.13万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0817965&HistoricalAwards=false
• 关键词: Collaborative; Research; Quantum; Decision; Theory

Research on human judgment and decision making has revealed a number of paradoxical findings that have resisted explanation under a common theoretical framework. These include violations of the sure thing axiom of decision making, interactions between inferences and decisions, violations of the reduction axiom of decision making, violations of the conjunctive and disjunctive axioms of probability theory, and order effects on judgments. In the past, separate and disconnected explanations have been proposed using variants of classic decision theory. This research proposes a unifying explanation for all of these paradoxical results based on a new quantum decision theory. Classic decision theory is based on classic probability theory. Probabilities are assigned to events defined as subsets of a universal set, which obey all the laws of Boolean algebra. Quantum decision theory is based on quantum probability theory. Probabilities are assigned to events defined as subspaces of a Hilbert space, which obey all the laws of Boolean algebra except the distributive axiom. Following from the distributive axiom, classic probability theory adheres to one of its most important theorems, the law of total probability. Because quantum logic does not have to obey the distributive law, quantum probabilities do not have to obey the law of total probability. Instead, quantum probability theory must obey another law called the doubly stochastic law, which the classic probability model does not obey. Hence, the two probability theories are fundamentally different and the critical question is which set of rules provides a better description of human behavior. The immediate goal of this research is to rigorously compare decision models built upon classical probability theory with those built from quantum probability theory. To rigorously compare quantum versus classical probability models of decision making, a series of experiments will be conducted. The experiments focus on tests of the law of total probability and tests of the law of double stochasticity, where the two classes of models make major and qualitatively different predictions. The research will accomplish three objectives: (1) develop a new quantum theory of human inference and decision making, (2) conduct new empirical tests of the fundamental laws of total probability and double stochasticity using human inference and decision behavior, and (3) rigorously compare and contrast classic versus quantum models of decision making with respect to the new empirical findings. A quantum or classic model will be preferred only if it provides a superior scientific explanation of the phenomena with respect to both accuracy and parsimony.The broad and long-term goal of this research program is to break new ground and pioneer a new path by building probabilistic and dynamic systems for social and behavioral sciences from quantum rather than classical probability principles. Previously, theorists in these fields have relied on mathematical models (e.g. stochastic differential equations) based on fundamental assumptions borrowed from classical physics. What are these fundamental assumptions? Are they overly restrictive? Social and behavioral scientists also face findings that remain paradoxical from a classic probability point of view. These paradoxes suggest that measurements in these fields may not always obey the law of total probability and entail different assumptions. This program of research also will contribute to the training of students at the undergraduate, graduate, and post doctoral levels at two major state universities. In addition to student training, the investigators will make an effort to train scientists in the area quantum cognition. They have conducted a full day tutorial at the annual Cognitive Science meeting and they plan to continue these tutorials in the future. They also plan to organize a special issue on Quantum Cognition in the Journal of Mathematical Psychology. New graduate courses on quantum cognition and decision making will be prepared and presented at the graduate level, and finally, a resource web site will be developed with tutorial and reference information on quantum theory for social and behavioral sciences.

对人类判断和决策的研究揭示了一些自相矛盾的发现，这些发现拒绝在共同的理论框架下进行解释。这些问题包括违反决策的确定性公理、推论和决策之间的相互作用、违反决策的约化公理、违反概率论的合取和析取公理以及对判断的顺序影响。在过去，使用经典决策理论的变体提出了独立的和不相关的解释。这项研究基于一种新的量子决策理论，对所有这些矛盾的结果提出了统一的解释。经典决策理论是以经典概率论为基础的。概率被分配给被定义为泛集的子集的事件，这些事件遵守布尔代数的所有定律。量子决策理论是建立在量子概率理论基础上的。概率被分配给定义为希尔伯特空间的子空间的事件，这些事件遵守布尔代数的所有定律，但分配公理除外。经典概率论从分配公理出发，遵循其最重要的定理之一--全概率定律。因为量子逻辑不一定要服从分布定律，所以量子概率也不一定要服从全概率定律。相反，量子概率理论必须遵守另一个称为双随机定律的定律，而经典概率模型并不遵守这个定律。因此，这两种概率理论从根本上是不同的，关键问题是哪一套规则能更好地描述人类行为。这项研究的直接目标是严格比较建立在经典概率理论和量子概率理论基础上的决策模型。为了严格比较决策的量子概率模型和经典概率模型，将进行一系列实验。实验的重点是检验全概率定律和双随机性定律，这两类模型做出主要和定性不同的预测。这项研究将完成三个目标：(1)发展一种新的人类推理和决策的量子理论；(2)利用人类的推理和决策行为对全概率和双随机性的基本规律进行新的经验检验；(3)根据新的经验发现，严格比较经典决策模型和量子决策模型。量子或经典模型只有在精确度和简洁性方面对现象提供了卓越的科学解释时才会受到青睐。这项研究计划的广泛和长期目标是通过从量子而不是经典概率原理为社会和行为科学建立概率和动态系统来开辟新的道路。以前，这些领域的理论家依赖于基于借用经典物理学的基本假设的数学模型(例如随机微分方程式)。这些基本假设是什么？他们是不是限制太多了？从经典概率的角度来看，社会科学家和行为科学家也面临着自相矛盾的发现。这些悖论表明，在这些领域的测量可能并不总是服从全概率定律，并需要不同的假设。这一研究计划还将有助于两所主要州立大学的本科生、研究生和博士后水平的培养。除了学生培训外，研究人员还将努力培训量子认知领域的科学家。他们已经在一年一度的认知科学会议上进行了一整天的指导，他们计划在未来继续这些指导。他们还计划在《数学心理学》杂志上组织一期关于量子认知的特刊。将在研究生一级编写和介绍新的量子认知和决策研究生课程，最后将开发一个资源网站，提供社会科学和行为科学的量子理论教程和参考信息。