Notice how none of these difficulties arise if you adopt the approach I had posted recently about, that you do not change the world, you discover what possible subjective world you live in. The question is always about what world model the agent has, not about the world itself, and about discovering more about that world model.
In the Parfit’s hitchhiker problem with the driver who is a perfect predictor, there is no possible world where the hitchhiker gets a lift but does not pay. The non-delirious agent will end up adjusting their world model to “Damn, apparently I am the sort of person who attempts to trick the driver, fails and dies” or “Happy I am the type of person who precommits to paying”, for example. There are many more possible worlds in that problem if we include the agents whose world model is not properly adjusted based on the input. In severe cases this is known as psychosis.
Similarly, “What if the 1000th digit of Pi were even?” is a question about partitioning possible worlds in your mind. Notice that there are not just two classes of those:
These classes include the possible worlds where you learn that the 1000th digit of Pi is even, the worlds where you learn that it is odd, the worlds where you never bother figuring it out, the worlds where you learned one answer, but then had to reevaluate it, or example, because you found a mistake in the calculations. There are also low-probability possible worlds, like those where Pi only has 999 digits, where the 1000th digit keeps changing, and so on. All those are possible world models, just some are not very probable apriori for the reference class of agents we are interested in.
...But that would be radically changing your world model from “there is the single objective reality about which we ask questions” to “agents are constantly adjusting models, and some models are better than others at anticipating future inputs.”
I’m not sure sure that it solves the problem. The issue is that in the case where you always choose “Don’t Pay” it isn’t easy to define what the predictor predicts as it is impossible for you to end up in town. The predictor could ask what you’d do if you thought the predictor was imperfect (as then ending up in town would actually be possible), but this mightn’t represent how you’d behave against a perfect predictor.
(But further, I am working within the assumption that everything is deterministic and that you can’t actually “change” the world as you say. How have I assumed the contrary?)
Notice how none of these difficulties arise if you adopt the approach I had posted recently about, that you do not change the world, you discover what possible subjective world you live in. The question is always about what world model the agent has, not about the world itself, and about discovering more about that world model.
In the Parfit’s hitchhiker problem with the driver who is a perfect predictor, there is no possible world where the hitchhiker gets a lift but does not pay. The non-delirious agent will end up adjusting their world model to “Damn, apparently I am the sort of person who attempts to trick the driver, fails and dies” or “Happy I am the type of person who precommits to paying”, for example. There are many more possible worlds in that problem if we include the agents whose world model is not properly adjusted based on the input. In severe cases this is known as psychosis.
Similarly, “What if the 1000th digit of Pi were even?” is a question about partitioning possible worlds in your mind. Notice that there are not just two classes of those:
These classes include the possible worlds where you learn that the 1000th digit of Pi is even, the worlds where you learn that it is odd, the worlds where you never bother figuring it out, the worlds where you learned one answer, but then had to reevaluate it, or example, because you found a mistake in the calculations. There are also low-probability possible worlds, like those where Pi only has 999 digits, where the 1000th digit keeps changing, and so on. All those are possible world models, just some are not very probable apriori for the reference class of agents we are interested in.
...But that would be radically changing your world model from “there is the single objective reality about which we ask questions” to “agents are constantly adjusting models, and some models are better than others at anticipating future inputs.”
I’m not sure sure that it solves the problem. The issue is that in the case where you always choose “Don’t Pay” it isn’t easy to define what the predictor predicts as it is impossible for you to end up in town. The predictor could ask what you’d do if you thought the predictor was imperfect (as then ending up in town would actually be possible), but this mightn’t represent how you’d behave against a perfect predictor.
(But further, I am working within the assumption that everything is deterministic and that you can’t actually “change” the world as you say. How have I assumed the contrary?)