SELECT * FROM (SELECT id, user, MAX(score) FROM table_1 GROUP BY user) AS sub ORDER BY 'sub.score' ASC;
	
+-----------------------+
| id | score | username |
+-----------------------+
| 1  |    15 |     mike |
| 2  |    23 |     tom  |
| 3  |    16 |     mike |
| 4  |    22 |     jack |

etc..
	
3 mike 16
2 tom  23
4 jack 22
	
3 mike 16
4 jack 22
2 tom  23
	
SELECT *
FROM (SELECT id, user, MAX(score) AS score
      FROM table_1
      GROUP BY user
     ) AS sub
ORDER BY sub.score ASC;