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In Decision 3012 (stop reading if you do not want spoilers):
Senator Travers uses the time paradox code from Bender's Big Score to go back in time to stop Nixon, and then he disappears when he won --- but shouldn't he have survived as a Time Paradox Duplicate????
Why did he suddenly cease to exist?
The whole idea of a time paradox duplicate is that they don't survive, so that paradoxes (paradoxi?) can be avoided. The duplicates are filled with doom radiation that eventually destroys them. The best explanation would be that the fulfillment of Senator Travers' "doom" was that he simply blinked out of existence. Granted, this is different than most other characters who met their doom in more violent fashions, but who's to say what the whims and follies of doom may be.
Also, he did survive for quite a long time as a duplicate: he had time enough to go to Harvard, become a community organizer, become a senator, and run for President. That's a long time to dodge doom for. Perhaps the doom radiation starts to really kick in only when a duplicate gets too close to triggering a paradox.
Bender quickly explained it at the end of the episode... Once Travers won, then Nixon wouldn't have put up the fence, thus Travers never would have been sent in the first place.
He was a time travel duplicate, therefore was doomed. This is not the reason he blanked out.
Instead, this is an instance of the grandfather paradox, he went back in time and changed future to prevent him from going back in time.
The resolution to the paradox chosen by futurama was that as he changed his own destiny, he ceased to exist. This is similar to the time travel rules in the "back to the future" movies. It's still consistent with past episodes (just)!
This is my opinion. Technically, the Paradox duplicate was the baby. Since Travers was the one in the Time Sphere going back in time. An example would be that Lars was the paradox duplicate of Fry when Fry went back in time to eat the pizza. Also, I think that paradox duplicates is only doomed when the original or another paradox duplicate is near. That would explain why Lars survived so long in the 21st Century.
The writers of Futurama killed Travers to give a message to the public, saying that the changing leaders won't change the world. Or something like that.
The point of Travers going back in time was to stop Nixon from winning the presidency of earth resulting in no more foreign aliens to work for them for cheap. As a result robots would be forced to do the work which results in an all out terminator style apocalyptic world run by Bender. The fact that Travers won meant he would not have been sent back in the future to save the present-past from Nixon hence defeating the purpose of him being there in the first place. Its politics 101. Also, it would only result in infinite loops like the fact that fry is not the same fry from the first time he went to the future but a replica of multiple times he's died and been reborn thru time travel. Hence there are more than one fry in the world, Lars was one good example.
