An allocation rule is ‘consistent’ if the recommendation it makes for each problem ‘agrees’ with the recommendation it makes for each associated reduced problem, obtained by imagining some agents leaving with their assignments. Some authors have described the consistency principle as a ‘fairness principle’. Others have written that it is not about fairness, that it should be seen as an ‘operational principle’. We dispute the particular fairness interpretations that have been offered for consistency, but develop a different and important fairness (...) foundation for the principle, arguing that it can be seen as the result of adding ‘some’ efficiency to a ‘post-application’ and efficiency-free expression of solidarity in response to population changes. We also challenge the interpretations of consistency as an operational principle that have been given, and here identify a sense in which such an interpretation can be supported. We review and assess the other interpretations of the principle, as ‘robustness’, ‘coherence’ and ‘reinforcement’. (shrink)