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Free choice (or statistical independence) assumption in a hidden variablemodel (HVM) means that the settings chosen by experimenters do not depend onthe values of the hidden variable. The assumption of context-independent (CI)mapping in an HVM means that the results of a measurement do not depend onsettings for other measurements. If the measurements are spacelike separated,this assumption is known as local causality. Both free choice and CI mappingassumptions are considered necessary for derivation of the Bell-type criteriaof contextuality/nonlocality. It is known, however, for a variety of specialcases, that the two assumptions are not logically independent. We show here, incomplete generality, for any system of random variables with or withoutdisturbance/signaling, that an HVM that postulates CI mapping is equivalent toan HVM that postulates free choice. If one denies the possibility that a givenempirical scenario can be described by an HVM in which measurements depend onother measurements' settings, free choice violations should be denied too, andvice versa.  KEYWORDS: Contextuality; context-independent mapping; free choice; localcausality; nonlocality.

Context-independent mapping and free choice are equivalent