MySQL order by multiple columns ignoring last order by directive

Question

When using the following query:

SELECT id, rater_id, product_id, is_valid  
FROM `ratings` 
WHERE (`ratings`.element_id = 3151) 
ORDER BY id DESC, product_id DESC, is_valid ASC;

i would expect that the result set will first be sorted by id first, then by product_id and then by is_valid. what actually happens is that the result set is indeed ordered, but the is_valid column in the results appears to be sorted by DESC, not by ASC. tried using both ASC and DESC but the result set stays the same.

+------------------+--------------+------+-----+---------+----------------+
| Field            | Type         | Null | Key | Default | Extra          |
+------------------+--------------+------+-----+---------+----------------+
| id               | int(11)      | NO   | PRI | NULL    | auto_increment |
| user_id          | int(11)      | NO   | MUL | NULL    |                |
| product_id       | int(11)      | YES  | MUL | NULL    |                |
| value            | tinyint(4)   | YES  | MUL | NULL    |                |
| rater_id         | int(11)      | YES  |     | NULL    |                |
| comment          | varchar(350) | YES  |     | NULL    |                |
| created_at       | datetime     | YES  |     | NULL    |                |
| updated_at       | datetime     | YES  |     | NULL    |                |
| element_id       | int(11)      | YES  | MUL | NULL    |                |
| is_valid         | tinyint(1)   | YES  | MUL | 0       |                |
+------------------+--------------+------+-----+---------+----------------+

Answer 1

The id field is an [unique auto incremental] primary key. This means that regardless of the values product_id and is_valid has, the order of id will render the other two ordering rules useless.

What I think is that you probably don't understand that the ORDER BY clause works as a nested ordering and not as an independent ordering of the values of the columns.