A decision maker chooses in a probabilistic manner if she does not necessarily prefer the same choice alternative when repeatedly presented with the same choice set. Probabilistic choice may occur for a variety of reasons such as unobserved attributes of choice alternatives, imprecision of preferences, or random errors/noise in decisions. The Luce choice model (also known as strict utility or multinomial logit) is derived from the choice axiom (also known as the independence from irrelevant alternatives). This axiom postulates that the relative likelihood of choosing one choice alternative A over another choice alternative B is not affected by the presence or absence of other choice alternatives in the choice set. This paper presents a dual choice axiom: the relative probability of NOT choosing A over the probability of NOT choosing B is independent from irrelevant alternatives. A new model of probabilistic choice is derived from this dual axiom. This model coincides with Luce’s choice model only in the case of a binary choice. The new model has similar properties as the Luce choice model: the higher is the utility of a choice alternative, the higher is the probability that a decision maker chooses this alternative and the lower is the probability that he or she chooses any other alternative. The new model differs from the Luce choice model in two aspects: utility of choice alternatives is bounded (from above and below) and choice probabilities are more sensitive to differences in utility of choice alternatives.

中文翻译：

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双重选择公理和概率选择

如果决策者在反复展示相同的选择集时不一定喜欢相同的选择，则以概率方式进行选择。可能会由于多种原因而发生概率选择，例如未观察到的选择替代属性，偏好的不精确性或决策中的随机错误/噪声。卢斯选择模型（也称为严格效用或多项式对数）从选择公理（也称为与无关选择的独立性）派生。该公理假定，选择集中存在或不存在其他选择备选方案，不影响选择一个选择备选方案A相对于另一个选择备选方案B的相对可能性。本文提出了双重选择公理：不选择A的相对概率比不选择B的概率独立于无关的选择。从这种双重公理推导出了一种新的概率选择模型。仅在二元选择的情况下，此模型才与Luce的选择模型相吻合。新模型与卢斯选择模型具有相似的属性：选择替代方案的效用越高，决策者选择该替代方案的可能性就越高，而他或她选择任何其他替代方案的可能性就越低。新模型在两个方面与Luce选择模型不同：选择替代品的效用是有界的（上下），选择概率对选择替代品的效用更敏感。从这种双重公理推导出了一种新的概率选择模型。仅在二元选择的情况下，此模型才与Luce的选择模型相吻合。新模型与卢斯选择模型具有相似的属性：选择替代方案的效用越高，决策者选择该替代方案的可能性就越高，而他或她选择任何其他替代方案的可能性就越低。新模型在两个方面与Luce选择模型不同：选择替代品的效用是有界的（上下），选择概率对选择替代品的效用更敏感。从这种双重公理推导出了一种新的概率选择模型。仅在二元选择的情况下，此模型才与Luce的选择模型相吻合。新模型与卢斯选择模型具有相似的属性：选择替代方案的效用越高，决策者选择该替代方案的可能性就越高，而他或她选择任何其他替代方案的可能性就越低。新模型在两个方面与Luce选择模型不同：选择替代品的效用是有界的（上下），选择概率对选择替代品的效用更敏感。决策者选择该替代方案的可能性越高，则他或她选择任何其他替代方案的可能性就越低。新模型在两个方面与Luce选择模型不同：选择替代品的效用是有界的（上下），选择概率对选择替代品的效用更敏感。决策者选择该替代方案的可能性越高，则他或她选择任何其他替代方案的可能性就越低。新模型在两个方面与Luce选择模型不同：选择替代品的效用是有界的（上下），选择概率对选择替代品的效用更敏感。