Dumbledore wished to die without the allegiance of the Elder Wand to pass on to someone else; he believed that if he planned his death with Snape, the Elder Wand wouldn't recognize Snape as its new master (since he didn't defeat Dumbledore); the Elder Wand would thus have no master and its true power would be lost forever.
Except things didn't go according to plan, since Draco defeated Dumbledore and became the master of the Elder Wand. But this was actually a good thing, because due to a series of contrived and convenient coincidences, Harry ended being the master of the Elder Wand, which caused the Wand to refuse to kill Harry, its master. Like Harry says in the final chapter, Dumbledore's plan backfired, but it backfired against Riddle.
Ok, but now suppose everything went according to Dumbledore's plan. The power of the Elder Wand is lost. Voldemort may or may not end realizing this, but, regardless, the Elder Wand will not backfire when used against Harry because Harry isn't its master. How exactly did Dumbledore intend Harry to defeat Voldemort?