Retrieve title from rows with a maximum count in other columns
Depending on your exact requirements, something along these lines should work:
Subqueries to determine most common attributes
SELECT DISTINCT title
FROM   archived
WHERE  showurl = (
   SELECT showurl
   FROM   archived
   GROUP  BY 1
   ORDER  BY count(*) DESC, 1
   LIMIT  1
   )
AND    reference = (
   SELECT reference
   FROM   archived
   GROUP  BY 1
   ORDER  BY count(*) DESC, 1
   LIMIT  1
   );

I added DISTINCT to the outer SELECT to fold duplicate titles. It's undefined what you need exactly.
Shorter with window functions
A more modern / sophisticated / elegant approach would be with two window functions in the ORDER BY clause, allowing for a very terse query:
SELECT title
FROM   archived
ORDER  BY count(*) OVER (PARTITION BY showurl)   DESC
         ,count(*) OVER (PARTITION BY reference) DESC
LIMIT 1;

Not necessarily faster than the first solution, though.
Again, guessing what you might want exactly, I only retrieve a single winning title.
The trick here is to partition the rows by showurl and reference, run a count over each partition and order descending by that count. This way, you can determine a winner in a single query level.
This will not work, if there is no row with the most common showurl and the most common reference at the same time. Again, exact requirements would be needed ...
-&gt; SQLfiddle demo.