How stable is a renovation ranking when priorities change? TOPSIS preference mapping and alternative-set tests for an anonymised building

A renovation package that performs best on one indicator need not remain preferred when investment and several environmental indicators are considered together. This paper examines six cumulative packages from a confidential nonresidential energy consultancy report using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Total investment, reported annual CO2 and reported annual NOx are treated as minimisation criteria. Vector normalisation, weighted Euclidean distance and observed ideal points are specified explicitly. Equal criterion weights place the fourth package first with a closeness score of approximately 0.6080, only 0.00385 above the final package. Illustrative cost-, carbon- and NOx-oriented profiles instead select the first, fifth and sixth packages respectively. Across a 231-point weight grid, every package is selected at least once; the final package leads at 112 grid points, which is a geometric count rather than a probability of stakeholder preference. Removing the first package reverses the order of the fourth and sixth packages even though their data and the weights remain unchanged. Replacing total investment by energy-related additional cost also changes rankings and weight-grid coverage. The study therefore presents conditional preference maps instead of a universal winner. It distinguishes the report's modelled emissions from local air-quality observations and identifies stakeholder weights, cost boundaries and technical feasibility as prerequisites for a binding decision.