My original comment had two examples, one had no coinflips, and the other had two coinflips. You seem to be talking about some other scenario which has one coinflip?
The structure I have in mind is a branching tree of time, where each branch has a measure. The root (the moment before any occurrences of time travel) has measure 1, and the measure of each branch is the sum of measures of its descendants. An additional law is that measure is “conserved” through time travel, i.e. when a version of you existing in a branch with measure p travels into the past, the past branches at the point of your arrival, so that your influence is confined to a branch of measure p (which may or may not eventually flow into the branch you came from, depending on other factors). So for example if you’re travelling to prevent a disaster that happened in your past, your chance of success is no higher than the chance of the disaster happening in the first place.
In the scenarios I have looked at, these conditions yield enough linear equations to pin down the measure of each branch, with no need to go through Markov chains. But the general case of multiple time travelers gets kinda hard to reason about. Maybe Markov chains can give a proof for that case as well?
But the general case of multiple time travelers gets kinda hard to reason about.
Since each time-travel event forks the universe, with multiple time travelers it’s a question of whether the the second time-traveler is “fork-traveling” as well.
My original comment had two examples, one had no coinflips, and the other had two coinflips. You seem to be talking about some other scenario which has one coinflip?
The structure I have in mind is a branching tree of time, where each branch has a measure. The root (the moment before any occurrences of time travel) has measure 1, and the measure of each branch is the sum of measures of its descendants. An additional law is that measure is “conserved” through time travel, i.e. when a version of you existing in a branch with measure p travels into the past, the past branches at the point of your arrival, so that your influence is confined to a branch of measure p (which may or may not eventually flow into the branch you came from, depending on other factors). So for example if you’re travelling to prevent a disaster that happened in your past, your chance of success is no higher than the chance of the disaster happening in the first place.
In the scenarios I have looked at, these conditions yield enough linear equations to pin down the measure of each branch, with no need to go through Markov chains. But the general case of multiple time travelers gets kinda hard to reason about. Maybe Markov chains can give a proof for that case as well?
Since each time-travel event forks the universe, with multiple time travelers it’s a question of whether the the second time-traveler is “fork-traveling” as well.