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Scale-invariance is an open problem in many computer vision subfields. For example, object labels should remain constant across scales, yet model predictions diverge in many cases. This problem gets harder for tasks where the ground-truth labels change with the presentation scale. In image quality assessment (IQA), downsampling attenuates impairments, e.g., blurs or compression artifacts, which can positively affect the impression evoked in subjective studies. To accurately predict perceptual image quality, cross-resolution IQA methods must therefore account for resolution-dependent errors induced by model inadequacies as well as for the perceptual label shifts in the ground truth. We present the first study of its kind that disentangles and examines the two issues separately via KonX, a novel, carefully crafted cross-resolution IQA database. This paper contributes the following: 1. Through KonX, we provide empirical evidence of label shifts caused by changes in the presentation resolution. 2. We show that objective IQA methods have a scale bias, which reduces their predictive performance. 3. We propose a multi-scale and multi-column DNN architecture that improves performance over previous state-of-the-art IQA models for this task, including recent transformers. We thus both raise and address a novel research problem in image quality assessment.