Distributional properties of cost allocation rules in multi-family energy retrofits: Evidence from 4 million apartments

Collective decisions to retrofit multi-family residential buildings require co-owners to agree on how the total cost is divided among dwellings, yet the distributional properties of alternative allocation rules have been insufficiently investigated at scale. Using harmonised Energy Performance Certificate (EPC) microdata covering over 4 million apartments in almost 450,000 buildings across Poland, England and Wales, and the Netherlands, we simulate five allocation rules: area-proportional, progressive-area, emissions-proportional, inefficiency-proportional, and Shapley-value allocation. For each building, we evaluate the resulting cost-share distributions using within-building inequality indices, size-progressivity measures, and cooperative-game-theoretic stability criteria. We find that performance-based rules produce within-building Gini coefficients 2 to 11 times higher than area-proportional allocation, with systematic variation across national building stocks. These rules are also less proportional in terms of dwelling size, assigning larger cost shares to smaller dwellings than their floor-area shares warrant. The Shapley rule, often advocated on cooperative-game-theoretic grounds, routinely allocates more to a single dwelling than that dwelling's stand-alone retrofit cost. The results show that cost-allocation rules generate distributional and stability consequences at policy-relevant magnitudes. For retrofit governance in multi-owner buildings, allocation design should therefore be treated as a central component of policy implementation rather than a technical-administrative choice.