This paper examines how the geometric structure of norms can be used to construct composite indicators in a coherent and transparent way. A central issue in the literature concerns the choice of aggregation rules, since many commonly used methods introduce discontinuities, assume full compensability between dimensions, or yield indicators with limited cardinal interpretability. Such features may have serious implications for the stability of rankings and for the interpretation of composite scores in policy and planning contexts. Within a norm-based framework, aggregation functions are continuous and endowed with a clear topological and metric structure, allowing multidimensional observations to be compared in a consistent manner. We show that all ℓ p norms with p ≥ 1 generate the same ordering on the positive cone, with the ℓ 1 norm acting as an upper bound within this family. This result highlights the geometric regularity underlying norm-based composite indicators and clarifies their relationship with other approaches commonly used in composite index construction.