Probabilistic Choice Induced by Strength of Preference
Probabilistic Choice Induced by Strength of Preference
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DOI：
10.1007/s42113-023-00176-3
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发表时间：
2023-09
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影响因子：
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通讯作者：
Daniel R. Cavagnaro;Michel Regenwetter
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文献类型：
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作者：
Daniel R. Cavagnaro;Michel Regenwetter
正如我们制定有关效用或偏好的详细理论一样，我们也应该仔细地对偏好强度进行理论分析。同样，由于行为本质上是不确定的，我们需要一个理论框架来理解选择概率。本文充实了一个简单的前提：更强烈的首选选项更有可能被选择。由此产生的无分布费希纳模型 (DFM) 避开了 Logit 和 Probit 等流行模型背后的便利性假设，揭示了核心决策理论的哪些方面在构建偏好强度的不同方式中保持不变，以及在偏好强度和选择概率之间的不同单调联系中保持不变。我们在统一的多面体几何空间中制定 DFM，允许直接比较完全不同的理论，例如后悔理论、预期效用理论和词典半序。几何表示还提供了参数计数之外的理论简约性的细致入微的视角。通过一系列例子，我们展示了带有和不带有效用的决策理论的 DFM 的推导和数学表征，以及人们可以从数据中得出的推论。我们展示了 DFM 如何提供多层定量方法来识别假设结构。我们重点介绍 DFM 保护研究人员免受过度指定模型导致的错误结论的具体案例。
Just as we formulate detailed theories of utility or preference, so too should we theorize carefully about strength of preference. Likewise, because behavior is inherently uncertain, we need a theoretical framework for understanding choice probabilities. This paper fleshes out the simple premise that more strongly preferred options are more likely to be chosen. The resultingdistribution-free Fechnerian models(DFMs) eschew convenience assumptions underlying popular models like the logit and probit, revealing which aspects of a core decision theory do or do not remain invariant across different ways of constructing strengths of preference, as well as across different monotonic links between those strengths of preference and choice probabilities. We formulate DFMs in a unifying polyhedral geometric space that allows for direct comparisons of theories that can be as categorically different as, say, regret theory, expected utility theory, and lexicographic semiorders. The geometric representation also provides a nuanced perspective on theoretical parsimony beyond parameter counting. Through a series of examples, we demonstrate the derivation and mathematical characterization of DFMs for decision theories with and without utilities and the inferences one can draw from data. We show how DFMs provide a multi-layered quantitative approach to the identifiability of hypothetical constructs. We highlight specific cases where DFMs protect the researcher against mistaken conclusions caused by overspecified models.