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Optimal Decision Fusion Under Order Effects

机译：订单效应下的最优决策融合

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This paper studies an optimal decision fusion problem with a group of human decision makers when anorder effectis present. The order effect refers to situations wherein the process of decision making by a human is affected by the order of decisions. In our set-up, all human decision makers, called observers, receive the same data which is generated by a common but unknown hypothesis. Then, each observer independently generates a sequence of decisions which are modeled by employing non-commutative probabilistic models of the data and their relation to the unknown hypothesis. The use of non-commutative probability models is motivated by recent psychological studies which indicate that these non-commutative probability models are more suitable for capturing the order effect in human decision making, compared with the classical probability model. A central decision maker (CDM) receives (possibly a subset of) the observers’ decisions and decides on the true hypothesis. The considered problem becomes an optimal decision fusion problem with observations modeled using a non-commutative (Von Neumann) probability model. The structure of the optimal decision rule at the CDM is studied under two scenarios. In the first scenario, the CDM receives the entire history of the observers’ decisions whereas in the second scenario, the CDM receives only the last decision of each observer. The perfromance of the optimal fusion rule is numerically evaluated and compared with the optimal fusion rule derived when using a classical probability model.
机译：当存在秩序效应时，本文研究了一组人类决策者的最优决策融合问题。顺序效应是指人的决策过程受决策顺序影响的情况。在我们的设置中，所有人类决策者（称为观察者）都将接收由相同但未知的假设所产生的相同数据。然后，每个观察者独立地生成一系列决策，这些决策通过采用数据的非交换概率模型及其与未知假设的关系来建模。非交换概率模型的使用受到近期心理学研究的推动，这些研究表明，与经典概率模型相比，这些非交换概率模型更适合于捕获人类决策中的顺序效应。中央决策者（CDM）接收观察者的决定（可能是其子集），并决定真实的假设。考虑到的问题变成了最优决策融合问题，其观测值使用非交换（冯·诺伊曼）概率模型建模。在两种情况下研究了CDM上最佳决策规则的结构。在第一种情况下，CDM接收观察者决定的全部历史记录，而在第二种情况下，CDM仅接收每个观察者的最后决定。对最佳融合规则的性能进行数值评估，并与使用经典概率模型得出的最佳融合规则进行比较。

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