Con una consulta como esta (simplificada para mayor claridad):

SELECT 'East' AS name, *
FROM events 
WHERE event_timestamp BETWEEN '2015-06-14 06:15:00' AND '2015-06-21 06:15:00' 

UNION

SELECT 'West' AS name, *
FROM events 
WHERE event_timestamp BETWEEN '2015-06-14 06:15:00' AND '2015-06-21 06:15:00'

UNION

SELECT 'Both' AS name, *
FROM events 
WHERE event_timestamp BETWEEN '2015-06-14 06:15:00' AND '2015-06-21 06:15:00'

Quiero personalizar el orden de las filas resultantes. Algo como:

ORDER BY name='East', name='West', name='Both'

O

ORDER BY 
    CASE
        WHEN name='East' THEN 1 
        WHEN name='West' THEN 2
        WHEN name='Both' THEN 3
        ELSE 4
    END;

Sin embargo, Postgres se queja con:

ERROR:  invalid UNION/INTERSECT/EXCEPT ORDER BY clause
DETAIL:  Only result column names can be used, not expressions or functions.
HINT:  Add the expression/function to every SELECT, or move the UNION into a FROM clause.

¿Tengo alguna alternativa?