We present a characterization of the Luce rule in terms of positivity and a new choice axiom called odds supermodularity that strengthens the regularity axiom. This new characterization illuminates a connection that goes unnoticed, and sheds light on the behavioral underpinnings of the Luce rule and its extensions from a different perspective. We show that odds supermodularity per se characterizes a structured extension of the Luce rule that accommodates zero probability choices. We identify the random choice model characterized via a stochastic counterpart of Plott (1973)'s path independence axiom, which strengthens odds supermodularity.

中文翻译：

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奇数超模和卢斯法则

我们从积极性和新的选择公理（称为赔率超模量）方面描述了Luce规则的特征，该公理加强了规则性公理。这种新的特征阐明了一个未被注意到的联系，并从不同的角度阐明了卢斯规则及其扩展的行为基础。我们表明，奇数超模数本身代表了适应零概率选择的Luce规则的结构化扩展。我们确定了随机选择模型，该模型的特征是Plott（1973）的路径独立性公理的随机对应物，该模型增强了赔率超模数。