In the context of the multidimensional measurement of complex phenomena, the major focus of the recent literature has been on the choice of the dimensions' weights and the shape of the aggregation function, while few studies have concentrated on how normalisation influences the results. With the aim of building a measure of Social Inclusion for 63 European regions in 2012, we adopt a standard linear aggregation framework and compare three alternative normalisation approaches: a data-driven min-max function and a data-driven Z-score, whose parameters depend solely on the available data, and an expert-based function, whose parameters are elicited through a survey at the University of Venice Ca' Foscari. Regardless of the adopted strategy, we show that normalisation plays a crucial part in defining variables' weighting. The data-driven strategies allocate a large relative weight to the longevity dimension, whereas the survey-driven results in a rather equal distribution of weights. Data-driven approaches produce trade-offs that are hard to interpret in economic terms and debatable from a social desirability perspective, thus constituting a positive analysis of Social Inclusion. Conversely, the expert-based normalisation is heavily affected by elicitation techniques, and allows for a normative interpretation of the resulting index. Furthermore, the three strategies lead to substantially different conclusions in terms of levels (both between and within countries) and distribution of Inclusion: numerous rank-reversals occur when switching the normalisation methods.