I just got an idea for an interesting fictional model of time travel, based on a combination of probabilities and consistent histories.

The simplest example would go like this. Imagine you step into the time machine, travel a minute into the past, and kill your younger self. At the moment of your arrival, the universe branches into two. Since the number (total weight?) of killers should be equal to the number of victims, the branches have probability 50% each. In one branch you live and become a killer, in the other you die.

Now let's take a more complex scenario. You flip a coin to decide whether you should step into the time machine, and another coin to kill or spare your past self. (Of course you have to travel to the moment before the first coinflip, otherwise this reduces to the previous scenario.) To figure out the probabilities, imagine that n people survive to flip the first coin. Then n/2 of them will step into the time machine and n/4 will become killers, which gives us n/4 victims. So you have a 1/5 chance of dying in this situation.

Is this model new? How far can we extend it consistently? What kinds of paradoxes can arise?