Measuring the generalization ability of Large Language Models (LLMs) is challenging due to data contamination. As models grow and computation becomes cheaper, ensuring tasks and test cases are unseen during training phases will become nearly impossible. We argue that knowledge-retrieval and reasoning tasks are not ideal for measuring generalization, as LLMs are not trained for specific tasks. Instead, we propose user behavior prediction, also a key aspect of personalization, as a theoretically sound, scalable, and robust alternative. We introduce a novel framework for this approach and test it on movie and music recommendation datasets for GPT-4o, GPT-4o-mini, and Llama-3.1-8B-Instruct. Results align with our framework's predictions, showing GPT-4o outperforms GPT-4o-mini and Llama, though all models have much room for improvement, especially Llama.