Strict priority for all open issues

For planning the work on open issues we need to set a strict priority for every open issue. That is, every open issue must either be more important or less important than every other open issue. It is not enough to set one of a finite set of priorities since we need to determine which issue to solve first even if both are Critical. These priorities are global per project. This way of strictly prioritizing issues is at the core of every agile methodology like XP, Crystal, and Scrum.

If this can be done using custom fields or otherwise, please point me to where I can learn how to do it, or give a descripton here.

Ideally I would like to be able to list open (or any) issues in a filter and get UP/DOWN arrows for every row to raise or lower the priority for this issue. Raising the priority of an issue (A) moves it one place up in the current list. The issue (B) shown directly above it before raising it ends directly below (A). Issues not shown in the current list that were between (A) and (B)are kept directly below (B). Vice versa for lowering the priority of an issue.

TOP/BOTTOM buttons would also be great, but may be limited by graphical design or screen space issues.

The permission to set priority could be associated with certain groups of users, in our case the CUSTOMER role.

This issue is very important to us, and I hope you will give it serious thought.

Another way of describing this priority system is ordinal priority.