I don't really fancy negotiating with somebody that is objectively wrong and in a higher position than me. Instead I will move the ground that they stand on.
The best game to play in this instance is to gain favour with their boss and anybody actively competing with them while passively disagreeing with them. You must passively disagree with them because the aim is to form a situation where you re-inforce their political opponents while appearing to be neutral - eventually they will come to you for support, and at this point they will be pliable. Something which will also help you gain authority is giving certain good ideas to other people whose interests will be in fighting your battles, however this is dangerous and you must make sure that they feel indebted to you.
If you don't want to kowtow to an idiot or beat them at their own game then simply quit and leave them to their mediocrity. There are likely to be a few places around where people will listen and use advice.
Edit: I obviously prefer just joining somewhere else without these kinds of insecure personalities, but my point was that political battles shouldn't be played in the light. You need to wear a cloak, you need to gather forces, and you need to resist the urge to slide the dagger in until others ask you to.
This leaves a bad taste in my mouth. I've seen quite a few people use this approach in an attempt to get their boss's job, irrespective of the boss's performance in their position. In general, I think that fighting your boss only leads to a draw, almost never to a win.
The best game to play in this instance is to gain favour with their boss and anybody actively competing with them while passively disagreeing with them. You must passively disagree with them because the aim is to form a situation where you re-inforce their political opponents while appearing to be neutral - eventually they will come to you for support, and at this point they will be pliable. Something which will also help you gain authority is giving certain good ideas to other people whose interests will be in fighting your battles, however this is dangerous and you must make sure that they feel indebted to you.
If you don't want to kowtow to an idiot or beat them at their own game then simply quit and leave them to their mediocrity. There are likely to be a few places around where people will listen and use advice.
Edit: I obviously prefer just joining somewhere else without these kinds of insecure personalities, but my point was that political battles shouldn't be played in the light. You need to wear a cloak, you need to gather forces, and you need to resist the urge to slide the dagger in until others ask you to.