The wedgie is inside the control lever housings and when the housing is tight on the handlebar the wedgie keeps it from rotating out of position while using. Sometimes you can get the housing to stay put by over tightening the small screw that pinches the housing on the handle bar but this is a really small screw and it threads into Aluminum threads so over tightening is not such a good idea.
The wedgies are often lost if you aren't looking for them when taking the handlebar housings off the handlebar.
If you do strip the threads in the housing it is possible to get a longer screw and attache with a nut instead of the Aluminum threads. This can be made to fit under the switch gear so it's not visible at all.