A common approach to personalization in large language models (LLMs) is to incorporate a subset of the user memory into the prompt at inference time to guide the model's generation. Existing methods select these subsets primarily using similarity between user memory items and input queries, ignoring how features actually affect the model's response distribution. We propose Response-Utility optimization for Memory Selection (RUMS), a novel method that selects user memory items by measuring the mutual information between a subset of memory and the model's outputs, identifying items that reduce response uncertainty and sharpen predictions beyond semantic similarity. We demonstrate that this information-theoretic foundation enables more principled user memory selection that aligns more closely with human selection compared to state-of-the-art methods, and models $400\times$ larger. Additionally, we show that memory items selected using RUMS result in better response quality compared to existing approaches, while having up to $95\%$ reduction in computational cost.