Alias scoping in SQL

I'm having an issue with a complex query on an SQLite3 database that I think has to do with a misunderstanding on my part of how to refer to columns in a results table returned by a select statement, especially when aliases are involved.

Here is an example table - a list of movie IDs with a row for each actor working on the movie:

CREATE TABLE movie_actor (imdb_id TEXT, actor TEXT);
INSERT INTO movie_actor VALUES('44r4', 'John Doe');
INSERT INTO movie_actor VALUES('44r4', 'Jane Doe');
INSERT INTO movie_actor VALUES('44r4', 'Jermaine Doe');
INSERT INTO movie_actor VALUES('44r4', 'Jacob Doe');
INSERT INTO movie_actor VALUES('55r5', 'John Doe');
INSERT INTO movie_actor VALUES('55r5', 'Jane Doe');
INSERT INTO movie_actor VALUES('55r5', 'Nathan Deer');
INSERT INTO movie_actor VALUES('66r6', 'Bob Duck');
INSERT INTO movie_actor VALUES('66r6', 'John Doe');
INSERT INTO movie_actor VALUES('66r6', 'Jermaine Doe');
INSERT INTO movie_actor VALUES('66r6', 'Jane Doe');
INSERT INTO movie_actor VALUES('77r7', 'John Doe');

I am trying to find out the how many times each pair of actors worked with each other across all movies. I decided to go about this with a self-join, but ran into issues where I would get record pairs such as "John Doe, Jane Doe, 3" and "Jane Doe, John Doe, 3" - this is really the same thing, and I wanted to only count the first version. This is the code that resulted:

SELECT DISTINCT 
    CASE WHEN d.actor_1 > d.actor_2 THEN d.actor_1 ELSE d.actor_2 END d.actor_1, 
    CASE WHEN d.actor_2 > d.actor_1 THEN d.actor_2 ELSE d.actor_1 END d.actor_2, 
    d.v 
FROM ( 
    SELECT c.actor_1 AS actor_1, c.actor_2 AS actor_2, COUNT(*) AS v 
    FROM ( 
        SELECT a.actor AS actor_1, b.actor AS actor_2 
        FROM movie_actor a JOIN movie_actor b ON a.imdb_id=b.imdb_id 
        ) AS c 
    WHERE c.actor_1 <> c.actor_2 
    GROUP BY c.actor_1, c.actor_2 
    HAVING COUNT(*) > 2 
    ORDER BY COUNT(*) DESC 
    LIMIT 20 
    ) 
    AS d

This doesn't run, but I can't figure out why. My assumption is that I am not using aliases properly, but I really don't know. Any ideas?

(SQL Fiddle link here)