Your definition of Hinginess doesn’t match the intuitive idea. In particular, you are talking about the range of possible values.
Suppose that you are at the first tick, making a decision. You have the widest range of “possible” options, but not all of those options are actually in your action space. Lets say that you personally will be dead by the second tick, and that you can’t influence the utility functions of any other agents with your decision now. You just get to choose which branch you go down. The actual path within that branch are entirely outside your control.
Consider a tree where the first ten options are ignored entirely, so the tree branches into 1024 identical subtrees. Then let the 11′th option completely control the utility. In this context, most of the hinginess is at tick 11. All someone at the first tick gets to choose is between two options, each of which are maybe 0 util or maybe lotsof util, as decided by factors outside your control, in other words, all the options have about the same expected utility.
It might be interesting to distinguish between “personal hingeyness” and “utilitarian hingeyness”. Humans are not utilitarians so we care mostly about stuff that’s happening in our own lives, when we die, our personal tree stops and we can’t get more hinges. But the “utilitarian hingeyness” continues as it describes all possible utility. I made this with population ethics in mind, but you could totally use the same concept for your personal life, but then the most hingey time for you and the most hingey time for everyone will be different.
I’m not sure I understand your last paragraph, because you didn’t clarify what you meant with the word “hingeyness”? If you meant by that “the range of total amount of utility you can potentially generate” (aka hinge broadness) or “the amount by which that range shrinks” (aka hinge reduction) It is possible to draw a tree where the first tick of an 11 tick tree has just as broad of a range as an option in the 10th tick. So the hinge broadness and the hinge reduction can be just as big in the 10th as in the 1st tick, but not bigger. I don’t think you’re talking about “hinge shift”, but maybe you were talking about hinge precipiceness instead in which case, yes that can totally be bigger in the 10th tick.
I was just trying to make the point that the bredth of available options doesn’t actually mean real world control.
Imagine a game where 11 people each take a turn to play in order. Each person can play either a 1 or a 0. Each player can see the moves of all the previous players. If the number of 1′s played is odd, everyone wins a prize. If you aren’t the 11′th player, it doesn’t matter what you pick, all that matters is whether or not the 11′th player wants the prize. (Unless all the people after you are going to pick their favourite numbers, regardless of the prize, and you know what those numbers are.
Your definition of Hinginess doesn’t match the intuitive idea. In particular, you are talking about the range of possible values.
Suppose that you are at the first tick, making a decision. You have the widest range of “possible” options, but not all of those options are actually in your action space. Lets say that you personally will be dead by the second tick, and that you can’t influence the utility functions of any other agents with your decision now. You just get to choose which branch you go down. The actual path within that branch are entirely outside your control.
Consider a tree where the first ten options are ignored entirely, so the tree branches into 1024 identical subtrees. Then let the 11′th option completely control the utility. In this context, most of the hinginess is at tick 11. All someone at the first tick gets to choose is between two options, each of which are maybe 0 util or maybe lotsof util, as decided by factors outside your control, in other words, all the options have about the same expected utility.
It might be interesting to distinguish between “personal hingeyness” and “utilitarian hingeyness”. Humans are not utilitarians so we care mostly about stuff that’s happening in our own lives, when we die, our personal tree stops and we can’t get more hinges. But the “utilitarian hingeyness” continues as it describes all possible utility. I made this with population ethics in mind, but you could totally use the same concept for your personal life, but then the most hingey time for you and the most hingey time for everyone will be different.
I’m not sure I understand your last paragraph, because you didn’t clarify what you meant with the word “hingeyness”? If you meant by that “the range of total amount of utility you can potentially generate” (aka hinge broadness) or “the amount by which that range shrinks” (aka hinge reduction) It is possible to draw a tree where the first tick of an 11 tick tree has just as broad of a range as an option in the 10th tick. So the hinge broadness and the hinge reduction can be just as big in the 10th as in the 1st tick, but not bigger. I don’t think you’re talking about “hinge shift”, but maybe you were talking about hinge precipiceness instead in which case, yes that can totally be bigger in the 10th tick.
I was just trying to make the point that the bredth of available options doesn’t actually mean real world control.
Imagine a game where 11 people each take a turn to play in order. Each person can play either a 1 or a 0. Each player can see the moves of all the previous players. If the number of 1′s played is odd, everyone wins a prize. If you aren’t the 11′th player, it doesn’t matter what you pick, all that matters is whether or not the 11′th player wants the prize. (Unless all the people after you are going to pick their favourite numbers, regardless of the prize, and you know what those numbers are.