I share your focus on the need to avoid arbitariness. I agree that recognition needs to be governed by a set of social recognition norms or it is simply arbitrary. That's why I am very fond of Axel Honneth's views on recognition, though I disagree with him on specifics. https://medium.com/inserting-philosophy/recognition-a-short-history-of-an-important-concept-5524e4dc8d60.