Beyond Marginal Distributions: A Framework to Evaluate the Representativeness of Demographic-Aligned LLMs

Large language models are increasingly used to represent human opinions, values, or beliefs, and their steerability towards these ideals is an active area of research. Existing work focuses predominantly on aligning marginal response distributions, treating each alignment evaluation example independently. While essential, this may overlook deeper latent structures that characterise real populations and underpin cultural values theories. We propose a framework for evaluating the representativeness of aligned models through multivariate correlation patterns in addition to marginal distributions. We show the value of our evaluation scheme by comparing two model steering techniques (persona prompting and demographic fine-tuning) and evaluating them against human responses from the World Values Survey. While the demographic fine-tuned model better approximates marginal response distributions, persona prompting performs marginally better at reproducing the empirical correlation structure between survey items. Despite this reversal, neither technique aligns with human correlation patterns. We conclude that representativeness is a distinct aspect of value alignment and an evaluation focused on marginals can mask structural failures, leading to overly optimistic conclusions about model representativeness.