Recent work has advocated for training AI models on ever-larger datasets, arguing that as the size of a dataset increases, the performance of a model trained on that dataset will correspondingly increase (referred to as “scaling laws”). In this paper, we draw on literature from the social sciences and machine learning to critically interrogate these claims. We argue that this scaling law relationship depends on metrics used to measure performance that may not correspond with how different groups of people perceive the quality of models' output. As the size of datasets used to train large AI models grows and AI systems impact ever larger groups of people, the number of distinct communities represented in training or evaluation datasets grows. It is thus even more likely that communities represented in datasets may have values or preferences not reflected in (or at odds with) the metrics used to evaluate model performance in scaling laws. Different communities may also have values in tension with each other, leading to difficult, potentially irreconcilable choices about metrics used for model evaluations---threatening the validity of claims that model performance is improving at scale. We end the paper with implications for AI development: that the motivation for scraping ever-larger datasets may be based on fundamentally flawed assumptions about model performance. That is, models may not, in fact, continue to improve as the datasets get larger---at least not for all people or communities impacted by those models. We suggest opportunities for the field to rethink norms and values in AI development, resisting claims for universality of large models, fostering more local, small-scale designs, and other ways to resist the impetus towards scale in AI.