Measuring wellbeing growth and convergence in multivariate ordered categorical worlds: Has there been any levelling up in the United Kingdom?

Measuring growth with ordered categorical variables is problematic due to their lack of cardinal measure and the equivocation and ambiguity inherent in the arbitrary attribution of cardinal scale to ordinal variates. Here, noting that the mean in a cardinal paradigm is the cumulation over its range of higher outcome probabilities and hence its growth is the rate of increase in those cumulated chances, application of the concept of probabilistic distance facilitates development of analogous implementable level and growth measures in ordinal paradigms that are independent of scale and unequivocal. An exemplifying analysis of the extent of 'Levelling Up' growth and convergence in Income, Health and Human resources in the regions of the United Kingdom is performed over the period 2010 to 2018 prior to the Covid outbreak. The results indicate that, while there is strong evidence of growth, there is little evidence of levelling up type growth and hence little evidence of Levelling Up in that nation.