Turn results of count distinct into something that can be aggregated - sql

Question

I have a table like this:
+----------+--------------+-------------+
| category | sub_category | customer_id |
+----------+--------------+-------------+
| A | AB2 | A876 |
| A | AB2 | A876 |
| A | AA1 | A876 |
| A | AA1 | A876 |
| A | AC3 | A756 |
| B | AB2 | A876 |
| B | AA1 | A756 |
| B | AB7 | A908 |
| C | AA1 | A756 |
| C | AB7 | A908 |
| C | AC3 | A908 |
+----------+--------------+-------------+
And I want to count distinct customers so I can easily do something like:
SELECT category, sub_category, COUNT(DISTINCT customer_id) as count_of_customers
FROM tbl
GROUP BY category, sub_category
And I get a report that gives me distinct customers for each sub_category and category. But these numbers can no longer be aggregated as there needs to be de-duplication if I just need distinct customers by category only.
For e.g customer_id = 'A876' will be counted twice in category='A' (once in sub_category = 'AB2' and once in sub_category = 'AA1') if I just sum the count_of_customers from my query result.
So here is the question, I would like to make these query results "aggregatable". Looking at the problem, it looks like this just isn't possible but I am wondering if there some clever way of distributing these results across categories? so that in my reporting layer (like an excel pivot table), I can get a result that counts 'A876' once in category='A' but counts it twice when I also include sub_category in the fields. Basically converting the results into something summable.
I should mention that this is an overly simplified example. The solution will need to generalize across n different categories and sub_categories.
I am looking for an output that would easily allow me to get either of the following results in something similar to a pivot table (think tableau-like reporting tools):
+----------+--------------------+
| category | distinct_customers |
+----------+--------------------+
| A | 2 |
| B | 3 |
| C | 2 |
+----------+--------------------+
+--------------+--------------------+
| sub_category | distinct_customers |
+--------------+--------------------+
| AA1 | 2 |
| AB2 | 1 |
| AB7 | 1 |
| AC3 | 2 |
+--------------+--------------------+
My immediate thought is to assign weights to a customer_id depending on how many categories and sub_categories it occurs in but I don't know exactly how I'd go about doing this.

Answer 1

You can do exactly what you want -- assigning weights. But this still won't aggregate correctly. Assuming there are no duplicates:
select category, sub_category,
count(distinct customer_id),
sum(1.0 / num_cs) as weighted_customers
from (select t.*,
count(*) over (partition by customer_id) as num_cs
from t
) t
group by category, sub_category;
This weights by both category and sub_category. Obviously, you can adjust the partition by to weight by just one or the other.