Changing One Field Updates 3 Other Fields, Use A Join?

i currently have a table like this..


user_id username app_id app2_id app3_id app4_id
1 john 3 4 5 6
2 mike 4 5 6 6
3 manager 4 5 6 6
4 vicepres 5 6 6 6
5 ceo 6 6 6 6
6 board 6 6 6 6


the basic pattern is... a user has approvers, and those approvers have approvers as well... i have 4 columns of approvers.. and if my first approver is the manager, then my second approver will be the managers approver and my third approver will be the managers approver's approver and so on..

on my actual page, i have select fields for the app, app2, app3, app4 and i need it so that when i change the very first app, it'll automatically update app2, app3, and app4

any ideas how i would do this? im pretty new to sql but im thinking i would use some type of join?

thanks