Creating an Index by summing percentiles This is probably a basic concept but i want to understand if it makes sense mathematically. I want to create an index on how much somebody spends at grocery stores. So for each person I calculate the total spend per shopL e.g. Asda, Tesco, Morrisons. For these three I then calculate the percentile they're in (so between 1 and 100).
Then I sum the 3 separate percentiles. I then re-percentile the sum.
In general, I have seen this method used a lot. Is it mathematically sound to sum percentiles?

This isn't much more than a comment, but here goes.
In your example, I can't see much advantage over adding the expenditure in various places and then if you wish working out where someone lies in the distribution of total expenditure. Similar comments apply more broadly.
All depends on what you want to capture in your measure, so on the goal of doing this in the first place. Mathematical soundness is not an issue. The mean across percentile ranks on different variables, or a percentile rank based on a sum of percentile ranks, is what it is: the question is whether either helps you in some project.
I can't comment on how commonly used this is in any literature.
