This paper provides a systematic account of the hidden variable models (HVMs) formulated to describe systems of random variables with mutually exclusive contexts. Any such system can be described either by a model with free choice but generally context-dependent mapping of the hidden variables into observable ones, or by a model with context-independent mapping but generally compromised free choice. These two types of HVMs are equivalent, one can always be translated into another. They are also unfalsifiable, applicable to all possible systems. These facts, the equivalence and unfalsifiability, imply that freedom of choice and context-independent mapping are no assumptions at all, and they tell us nothing about freedom of choice or physical influences exerted by contexts as these notions would be understood in science and philosophy. The conjunction of these two notions, however, defines a falsifiable HVM that describes non-contextuality when applied to systems with no disturbance or to consistifications of arbitrary systems. This HVM is most adequately captured by the term ‘context-irrelevance’, meaning that no distribution in the model changes with context. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

中文翻译：

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隐藏变量、自由选择、上下文无关等等

本文对隐藏变量模型 (HVM) 进行了系统说明，该模型旨在描述具有互斥上下文的随机变量系统。任何这样的系统都可以通过具有自由选择但通常依赖于上下文的隐藏变量到可观察变量的映射的模型来描述，或者通过具有上下文无关的映射但通常会损害自由选择的模型来描述。这两种类型的 HVM 是等效的，一种总是可以转换为另一种。它们也是不可证伪的，适用于所有可能的系统。这些事实，即等价性和不可证伪性，意味着选择自由和与上下文无关的映射根本不是假设，它们没有告诉我们任何有关选择自由或上下文施加的物理影响的信息，因为这些概念在科学和哲学中会被理解。然而，这两个概念的结合定义了一个可证伪的 HVM，当应用于无干扰的系统或任意系统的组合时，它描述了非上下文性。术语“上下文无关”最能充分地描述该 HVM，这意味着模型中的分布不会随上下文而变化。本文是“量子背景、因果关系和选择自由”主题的一部分。