Persona-assigned Large Language Models (LLMs) can adopt diverse roles, enabling personalized and context-aware reasoning. However, even minor demographic perturbations in personas, such as simple pronoun changes, can alter reasoning trajectories, leading to divergent sets of correct answers. Instead of treating these variations as biases to be mitigated, we explore their potential as a constructive resource to improve reasoning robustness. We propose CHOIR (Collaborative Harmonization fOr Inference Robustness), a test-time framework that harmonizes multiple persona-conditioned reasoning signals into a unified prediction. CHOIR orchestrates a collaborative decoding process among counterfactual personas, dynamically balancing agreement and divergence in their reasoning paths. Experiments on various reasoning benchmarks demonstrate that CHOIR consistently enhances performance across demographics, model architectures, scales, and tasks - without additional training. Improvements reach up to 26.4% for individual demographic groups and 19.2% on average across five demographics. It remains effective even when base personas are suboptimal. By reframing persona variation as a constructive signal, CHOIR provides a scalable and generalizable approach to more reliable LLM reasoning.