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Decision theory with prospect interference and entanglement

机译：具有潜在干扰和纠缠的决策理论

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摘要

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage's sure-thing principle, known as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested.
机译：我们提出了一种基于可分离希尔伯特空间数学理论的新型决策方法。这种数学结构捕获了复合前景叠加的效果，包括许多合并的意图，这使我们能够描述各种有趣的谬论和异常，这些谬论和异常已被报道来具体说明真实人类的决策。该理论的特征是纠结的决策，后续决策的不可交换性以及意图干扰。我们证明了在不确定性条件下进行决策时，由于意图的干扰，可以量化地解释对野蛮人的确定性原则的违反，即析取效应。使用我们得出的干扰交替定理，可以准确地预测在实验中观察到的分离效应，该定理将厌恶不确定性与抑制干扰概率的负面干扰项的出现联系起来。连词谬误也由干扰项的存在来解释。分析了一系列实验，结果表明与干扰效应的先验评估非常吻合。连词谬误也被证明是分离效应的充分条件，并提出了新颖的实验来测试两种效应之间的相互作用。

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