For updatelessness commitments to be advantageous, you need to be interacting with other agents that have a better-than-random chance of predicting your behavior under counterfactual circumstances. Agents have finite computational resources, and running a completely accurate simulation of another agent requires not only knowing their starting state but also being able to run a simulation of them at comparable speed and cost. Their strategic calculation might, of course, be simple, thus easy to simulate, but in a competitive situation if they have a motivation to be hard to simulate, then it is to their advantage to be as hard as possible to simulate and to run a decision process that is as complex as possible. (For example “shortly before the upcoming impact in our game of chicken, leading up to the last possible moment I could swerve aside, I will have my entire life up to this point flash before by eyes, hash certain inobvious features of this, and, depending on the twelfth bit of the hash, I will either update my decision, or not, in a way that it is unlikely my opponent can accurately anticipate or calculate as fast as I can”.)
In general, it’s always possible for an agent to generate a random number that even a vastly-computationally-superior opponent cannot predict (using quantum sources of randomness, for example).
It’s also possible to devise a stochastic non-linear procedure where it is computationally vastly cheaper for me to follow one randomly-selected branch of it than it is for someone trying to model me to run all branches, or even Monte-Carlo simulate a representative sample of them, and where one can’t just look at the algorithm and reason about what the net overall probability of various outcomes is, because it’s doing irreducibly complex things like loading random numbers into Turing machines or cellular automata and running the resulting program for some number of steps to see what output, if any, it gets. (Of course, I may also not know what the overall probability distribution from running such a procedure is, if determining that is very expensive, but then, I’m trying to be unpredictable.) So it’s also possible to generate random output that even a vastly-computationally-superior opponent cannot even predict the probability distribution of.
In the counterfactual mugging case, call the party proposing the bet (the one offering $1000 and asking for $100) A, and the other party B. If B simply publicly and irrevocably precommits to paying the $100 (say by posting a bond), their expected gain is $450. If they can find a way to cheat, their maximum potential gain from the gamble is $500. So their optimal strategy is to initially do a (soft) commit to paying the $100, and then, either before the coin is tossed, and/or after that on the heads branch:
Select a means of deciding on a probability p that I will update/renege after the coin lands if it’s a heads, and (if the coin has not yet been tossed) optionally a way I could signal that. This means can include using access to true (quantum) randomness, hashing parts of my history selected somehow (including randomly), hashing new observations of the world I made after the coin landed, or anything else I want.
Using << $50 worth of computational resources, run a simulation of party A in the tails branch running a simulation of me, and predict the probability distribution for their estimate of p. If the mean of that is lower than pthen go ahead and run the means for choosing. Otherwise, try again (return to step 1), or, if the computational resources I’ve spent are approaching $50 in net value, give up and pay A the $100 if the coin lands (or has already landed) heads.
Meanwhile, on the heads branch, party A is trying to simulate party B running this process, and presumably is unwilling to spend more than some fraction of $1000 in computational resources to doing this. If party B did their calculation before the coin toss and chose to emit a signal(or leaked one), then party A has access to that, but obviously not to anything that only happened on the heads branch after the outcome of the coin toss was visible.
So this turns into a contest of who can more accurately and cost effectively simulate the other simulating them, recursively. Since B can choose a strategy, including choosing to randomly select obscure features of their past history and make these relevant to the calculation, while A cannot, B would seem to be at a distinct strategic advantage in this contest unless A has access to their entire history.
For updatelessness commitments to be advantageous, you need to be interacting with other agents that have a better-than-random chance of predicting your behavior under counterfactual circumstances. Agents have finite computational resources, and running a completely accurate simulation of another agent requires not only knowing their starting state but also being able to run a simulation of them at comparable speed and cost. Their strategic calculation might, of course, be simple, thus easy to simulate, but in a competitive situation if they have a motivation to be hard to simulate, then it is to their advantage to be as hard as possible to simulate and to run a decision process that is as complex as possible. (For example “shortly before the upcoming impact in our game of chicken, leading up to the last possible moment I could swerve aside, I will have my entire life up to this point flash before by eyes, hash certain inobvious features of this, and, depending on the twelfth bit of the hash, I will either update my decision, or not, in a way that it is unlikely my opponent can accurately anticipate or calculate as fast as I can”.)
In general, it’s always possible for an agent to generate a random number that even a vastly-computationally-superior opponent cannot predict (using quantum sources of randomness, for example).
It’s also possible to devise a stochastic non-linear procedure where it is computationally vastly cheaper for me to follow one randomly-selected branch of it than it is for someone trying to model me to run all branches, or even Monte-Carlo simulate a representative sample of them, and where one can’t just look at the algorithm and reason about what the net overall probability of various outcomes is, because it’s doing irreducibly complex things like loading random numbers into Turing machines or cellular automata and running the resulting program for some number of steps to see what output, if any, it gets. (Of course, I may also not know what the overall probability distribution from running such a procedure is, if determining that is very expensive, but then, I’m trying to be unpredictable.) So it’s also possible to generate random output that even a vastly-computationally-superior opponent cannot even predict the probability distribution of.
In the counterfactual mugging case, call the party proposing the bet (the one offering $1000 and asking for $100) A, and the other party B. If B simply publicly and irrevocably precommits to paying the $100 (say by posting a bond), their expected gain is $450. If they can find a way to cheat, their maximum potential gain from the gamble is $500. So their optimal strategy is to initially do a (soft) commit to paying the $100, and then, either before the coin is tossed, and/or after that on the heads branch:
Select a means of deciding on a probability p that I will update/renege after the coin lands if it’s a heads, and (if the coin has not yet been tossed) optionally a way I could signal that. This means can include using access to true (quantum) randomness, hashing parts of my history selected somehow (including randomly), hashing new observations of the world I made after the coin landed, or anything else I want.
Using << $50 worth of computational resources, run a simulation of party A in the tails branch running a simulation of me, and predict the probability distribution for their estimate of p. If the mean of that is lower than pthen go ahead and run the means for choosing. Otherwise, try again (return to step 1), or, if the computational resources I’ve spent are approaching $50 in net value, give up and pay A the $100 if the coin lands (or has already landed) heads.
Meanwhile, on the heads branch, party A is trying to simulate party B running this process, and presumably is unwilling to spend more than some fraction of $1000 in computational resources to doing this. If party B did their calculation before the coin toss and chose to emit a signal(or leaked one), then party A has access to that, but obviously not to anything that only happened on the heads branch after the outcome of the coin toss was visible.
So this turns into a contest of who can more accurately and cost effectively simulate the other simulating them, recursively. Since B can choose a strategy, including choosing to randomly select obscure features of their past history and make these relevant to the calculation, while A cannot, B would seem to be at a distinct strategic advantage in this contest unless A has access to their entire history.