From what I understand, in the case of the Herfindahl-Hirschman index or other things of that nature, there can be two different distributions of market share that give the same index, for example. Ultimately, reducing it all to market share virtually prevents the work of the competition commissioner from doing its job, because it reduces the commissioner's tools to just one: a threshold.
On June 3rd, 2024. See this statement in context.