I quite like this model, it seems natural to me that to quantify hingeyness in this model would be by considering how different the probability distributions of the total utility at the end of time are. Things like how much the range contracts also seem to be decent quick approximations of this difference. There has actually been a lot of work on quantifying this difference between probability distributions, searches for statistical distance or “probability metrics” should give you results.
If we were to define hingeyness in this model using some notion of the distance between probability distributions it seems likely we would want this distance to have the properties of a metric. It’s not obvious to me which metric would be the best choice for this model though. The Wasserstein metric seems the easiest metric from the above link to implement to me.
Also mod-team, this comment isn’t visible underneath my post in any of my browsers. Is there any way to fix that?
EDIT: Thank you mod-team!
EDIT 2: It just occurred to me that some people may find the shift in range also important for hingeyness. I’ll illustrate what I mean with a new image:
Here the “range of possible utility in endings” tick 1 has (the first 10) is [0-10] and the “range of possible utility in endings” the first 0 has (tick 2) is [0-10] which is the same. Of course the probability has changed (getting an ending of 1 utility is not even an option anymore), but the minimum and maximum stay the same.
But we don’t care about just the endings, we care about the rest of the journey too. The width of the “range of the total amount of utility you could potentially experience over all branches (not just the endings)” can shrink or stay the same. But the range itself can shift. For example the lowest possible utility tick 1 can experience is 10->0->0 = 10 utility and the highest possible utility that it can experience is 10->0->10 = 20 utility. The difference between the lowest and highest is 10 utility. The lowest total utility that the 0 on tick 2 can experience is 0->0 = 0 utility and the highest is 0->10 = 10 utility, which is once again a difference of 10 utility.
The probability has changed: Ending with a weird number like 19 is impossible for the ‘0 on tick 2’. The probability for a good ending has also become much more favorable (50% chance to end with a 10 instead of 25% it was before). Probability is important for the precipiceness.
But while the width of the range stayed the same, the range itself has shifted downwards from [10-20] to [0-10]. Maybe this also an important factor in what some people call hingeyness? Maybe call that ‘hinge shift’?
This will effect the probability that you end up in certain futures and not others. I used the word precipiceness in my post to refer to high-risk high-reward probability distributions. Maybe it’s also important to have a word for a time in which the probability that we will generate low amounts of utility in the future is increasing. We call this “increase in x-risk” now because going extinct is most of the time a good way to ensure you will generate low amounts of utility. But as I showed in my post, you can have an awesome extinction and a horrible long existence. Maybe I shouldn’t be trying to attach words to all the different variants of probability distributions and just draw them instead.
To recap “the range of total amount of utility you can potentially generate” aka “hinge broadness” can:
1) Shrink by a certain amount (aka hinge reduction) this can be because the most amount of utility you can potentially generate is decreasing (I’ll call this “top-reduction”) or because the least amount of utility you can potentially generate is increasing (I’ll call this “bottom-reduction”). Top-reduction is bad, bottom-reduction is good.
2) Shift upward or downward in utility by a certain amount (aka hinge shift) Upward shift is good, downward shift is bad.
I quite like this model, it seems natural to me that to quantify hingeyness in this model would be by considering how different the probability distributions of the total utility at the end of time are. Things like how much the range contracts also seem to be decent quick approximations of this difference. There has actually been a lot of work on quantifying this difference between probability distributions, searches for statistical distance or “probability metrics” should give you results.
If we were to define hingeyness in this model using some notion of the distance between probability distributions it seems likely we would want this distance to have the properties of a metric. It’s not obvious to me which metric would be the best choice for this model though. The Wasserstein metric seems the easiest metric from the above link to implement to me.
That’s a very useful link, thank you.
Also mod-team, this comment isn’t visible underneath my post in any of my browsers. Is there any way to fix that?
EDIT: Thank you mod-team!
EDIT 2: It just occurred to me that some people may find the shift in range also important for hingeyness. I’ll illustrate what I mean with a new image:
(I can’t post images in comments so here is a link to the image I will use to illustrate this point)
Here the “range of possible utility in endings” tick 1 has (the first 10) is [0-10] and the “range of possible utility in endings” the first 0 has (tick 2) is [0-10] which is the same. Of course the probability has changed (getting an ending of 1 utility is not even an option anymore), but the minimum and maximum stay the same.
But we don’t care about just the endings, we care about the rest of the journey too. The width of the “range of the total amount of utility you could potentially experience over all branches (not just the endings)” can shrink or stay the same. But the range itself can shift. For example the lowest possible utility tick 1 can experience is 10->0->0 = 10 utility and the highest possible utility that it can experience is 10->0->10 = 20 utility. The difference between the lowest and highest is 10 utility. The lowest total utility that the 0 on tick 2 can experience is 0->0 = 0 utility and the highest is 0->10 = 10 utility, which is once again a difference of 10 utility.
The probability has changed: Ending with a weird number like 19 is impossible for the ‘0 on tick 2’. The probability for a good ending has also become much more favorable (50% chance to end with a 10 instead of 25% it was before). Probability is important for the precipiceness.
But while the width of the range stayed the same, the range itself has shifted downwards from [10-20] to [0-10]. Maybe this also an important factor in what some people call hingeyness? Maybe call that ‘hinge shift’?
This will effect the probability that you end up in certain futures and not others. I used the word precipiceness in my post to refer to high-risk high-reward probability distributions. Maybe it’s also important to have a word for a time in which the probability that we will generate low amounts of utility in the future is increasing. We call this “increase in x-risk” now because going extinct is most of the time a good way to ensure you will generate low amounts of utility. But as I showed in my post, you can have an awesome extinction and a horrible long existence. Maybe I shouldn’t be trying to attach words to all the different variants of probability distributions and just draw them instead.
To recap “the range of total amount of utility you can potentially generate” aka “hinge broadness” can:
1) Shrink by a certain amount (aka hinge reduction) this can be because the most amount of utility you can potentially generate is decreasing (I’ll call this “top-reduction”) or because the least amount of utility you can potentially generate is increasing (I’ll call this “bottom-reduction”). Top-reduction is bad, bottom-reduction is good.
2) Shift upward or downward in utility by a certain amount (aka hinge shift) Upward shift is good, downward shift is bad.