Large language models (LLMs) are increasingly used to simulate human opinions and survey responses, but their ability to reproduce population responses across cultures remains limited. Existing persona-based prompting methods typically rely on sociodemographic or personality traits, which are only indirect proxies for the values that shape human responses. We propose a value-based persona construction method that derives textual descriptors from survey responses capturing core cultural dimensions. By sampling value profiles from target populations and aggregating LLM responses across personas, we obtain population-level predictions grounded in observed value distributions. We further introduce a calibration procedure that improves response diversity while preserving estimated opinions. We show that our approach reduces prediction error across countries, with the largest improvements observed in underrepresented populations. This substantially narrows the performance gap between countries aligned with dominant LLM priors and those that are less represented in training data, while also yielding response distributions that closely match human diversity.