(Edit 2/note: the OP’s edits in response to this comment render this comment fairly irrelevant except as a more detailed explanation for why defining hingeyness in terms of total possible range (see: “2. Older decisions are hingier?”) doesn’t seem to make much sense/be very useful as a concept)
Apologies in advance if I’m misunderstanding your point; I’ve never analyzed “hingeyness” much, and so I’m not trying to advance a theory or necessarily contest your overall argument. However, one thing you said doesn’t sit well with me—namely, the part where you argue that older decisions are necessarily hingier, and that is part of why you think the definition regarding the “Hinge of History” is not very helpful. I can think of lots of situations, both real and hypothetical, where a decision at time X (say, “year 1980” or “turn 1“) has much less effect on both direct utility and future choices than a decision or set of decisions at time Y (say, “year 1999” or “turn 5”), in part because decision X may have (almost) no effect on the choices/options much later (e.g., it does not affect which options are available, it does not affect what effect the options have).
Take for hypothetical example a game where you are in a room with four computers, each labeled by a number (1-4). At the start of the game (point 1), only computer 1 is usable, but you can choose option 1a or option 1b. The following specifics don’t matter much for the argument I’m making, but suppose 1a produces +5 utility and turns on computer 2, and option 1b produces +3 utility and turns on computer 3. (Suppose computer 2 and computer 3 have options with utility in the ranges of +1 to +10.) However, regardless of what you do at point 1--whether you press either 1a or 1b—computer 4 also turns on. This is point 2 in the game. On computer 4, you have option 4a which produces −976,000 utility, and option 4b produces +865,000 utility. And then the game ends.
This paragraph is unnecessary if you understand the previous paragraph, but for a more real-world example, I would point to (original) Quiplash: although not as drastic as the hypothetical above, my family and I would often complain that the game was a bit unbalanced/frustrating due to how your performance/success really hinged on second phase of the game. The game has three phases, but the points in phase 2 are worth double those in phase 1, and (if I remember correctly) it was similarly much more important than phase 3. Your performance in phase 1 would not really/necessarily affect how well you did in later phases (with unimportant exceptions such as recurring jokes/figuring out what the audience likes).
I recognize that “*technically*” you may be able to represent such situations game-tree-theoretically by including it as a timeline with every possible permutation, but I would argue that doing so loses much of the theoretical idea(s) that the conceptualization of hingeyness (if not also some game theory models) ought to address: that some decisions’ availability and significance are relatively independent of other decisions. My choices at time “late lunch today” between eating a sandwich and a bowl of soup could technically be put on the same decision tree as my choices at time “(a few months from now)” between applying to grad school or applying to an internship, but I feel that the latter time should be recognized as more “Hingey.”
Edit 1: I do think that you begin to get at this issue/idea when you go into point 3, about decreases in range, I just still take issue with statements like “Older decisions are hingier.” If you were just posing it as a claim to challenge/test (and decided that it was incorrect/that it means we should define hingeyness in that way), I may have just misinterpreted as a claim or a conceptualization of hingeyness that you were trying to argue for.
The reason I find the definition not very useful is because it can be interpreted in so many different ways. The aim of this post was to show the four main ways you could interpreted it. When I read the definition my first interpretation was “hinge broadness”, while I suspect your interpretation was “hinge reduction”. I’m not saying that hinge broadness is the ‘correct’ definition of hingeyness, because there is no ‘correct’ definition of hingeyness until a community of language users has made it a convention. There is no convention yet so I’m purposefully splitting the concept into more quantifiable chunks in the hope that we can avoid the confusion that comes from multiple people using the same terms for different concepts. Since I failed to convey this I will slightly edit this post to clear it up for the next confused reader. I added one sentence, and tweaked another sentence and a subtitle. The old version of the post can be found on LessWrong.
I think those changes help clarify things! I just didn’t quite understand your intent with the original wording/heading. I think it is a good idea to try to highlight the potential different definitions for the concept, as well as issues with those definitions.
(Edit 2/note: the OP’s edits in response to this comment render this comment fairly irrelevant except as a more detailed explanation for why defining hingeyness in terms of total possible range (see: “2. Older decisions are hingier?”) doesn’t seem to make much sense/be very useful as a concept)
Apologies in advance if I’m misunderstanding your point; I’ve never analyzed “hingeyness” much, and so I’m not trying to advance a theory or necessarily contest your overall argument. However, one thing you said doesn’t sit well with me—namely, the part where you argue that older decisions are necessarily hingier, and that is part of why you think the definition regarding the “Hinge of History” is not very helpful. I can think of lots of situations, both real and hypothetical, where a decision at time X (say, “year 1980” or “turn 1“) has much less effect on both direct utility and future choices than a decision or set of decisions at time Y (say, “year 1999” or “turn 5”), in part because decision X may have (almost) no effect on the choices/options much later (e.g., it does not affect which options are available, it does not affect what effect the options have).
Take for hypothetical example a game where you are in a room with four computers, each labeled by a number (1-4). At the start of the game (point 1), only computer 1 is usable, but you can choose option 1a or option 1b. The following specifics don’t matter much for the argument I’m making, but suppose 1a produces +5 utility and turns on computer 2, and option 1b produces +3 utility and turns on computer 3. (Suppose computer 2 and computer 3 have options with utility in the ranges of +1 to +10.) However, regardless of what you do at point 1--whether you press either 1a or 1b—computer 4 also turns on. This is point 2 in the game. On computer 4, you have option 4a which produces −976,000 utility, and option 4b produces +865,000 utility. And then the game ends.
This paragraph is unnecessary if you understand the previous paragraph, but for a more real-world example, I would point to (original) Quiplash: although not as drastic as the hypothetical above, my family and I would often complain that the game was a bit unbalanced/frustrating due to how your performance/success really hinged on second phase of the game. The game has three phases, but the points in phase 2 are worth double those in phase 1, and (if I remember correctly) it was similarly much more important than phase 3. Your performance in phase 1 would not really/necessarily affect how well you did in later phases (with unimportant exceptions such as recurring jokes/figuring out what the audience likes).
I recognize that “*technically*” you may be able to represent such situations game-tree-theoretically by including it as a timeline with every possible permutation, but I would argue that doing so loses much of the theoretical idea(s) that the conceptualization of hingeyness (if not also some game theory models) ought to address: that some decisions’ availability and significance are relatively independent of other decisions. My choices at time “late lunch today” between eating a sandwich and a bowl of soup could technically be put on the same decision tree as my choices at time “(a few months from now)” between applying to grad school or applying to an internship, but I feel that the latter time should be recognized as more “Hingey.”
Edit 1: I do think that you begin to get at this issue/idea when you go into point 3, about decreases in range, I just still take issue with statements like “Older decisions are hingier.” If you were just posing it as a claim to challenge/test (and decided that it was incorrect/that it means we should define hingeyness in that way), I may have just misinterpreted as a claim or a conceptualization of hingeyness that you were trying to argue for.
The reason I find the definition not very useful is because it can be interpreted in so many different ways. The aim of this post was to show the four main ways you could interpreted it. When I read the definition my first interpretation was “hinge broadness”, while I suspect your interpretation was “hinge reduction”. I’m not saying that hinge broadness is the ‘correct’ definition of hingeyness, because there is no ‘correct’ definition of hingeyness until a community of language users has made it a convention. There is no convention yet so I’m purposefully splitting the concept into more quantifiable chunks in the hope that we can avoid the confusion that comes from multiple people using the same terms for different concepts.
Since I failed to convey this I will slightly edit this post to clear it up for the next confused reader. I added one sentence, and tweaked another sentence and a subtitle. The old version of the post can be found on LessWrong.
I think those changes help clarify things! I just didn’t quite understand your intent with the original wording/heading. I think it is a good idea to try to highlight the potential different definitions for the concept, as well as issues with those definitions.