What’s worse, stealing one cent each from 5,000,000 people, or stealing $49,999 from one person? (Let us further assume that money has some utility value.)
If we decide we can just add the diminished wealth together, the former is clearly one cent worse: $50,000 is stolen, as opposed to $49,999. But this doesn’t take into account that loss of utility grows with each cent lost from the same person. Losing one cent won’t bother me at all; everyone else who had a cent stolen would probably feel the same way. However, $49,999 from one person is enough to ruin their life: numerically, less was stolen overall, but the utility loss grows incredibly as it is concentrated.
Another case: is an eye-mote a second for a year (31,556,926 motes) in one person better than 31,556,927 motes spread out evenly among 31,556,927 people? The former case would involve serious loss of utilons, whereas a single mote is quickly fixed and forgotten: qualitatively different from constant irritation. The loss of utilons from dust motes can thus be concentrated and added, but not spread out and then added. (I think this may indicate time and memory plays a factor in this, since they do in the mechanism of suffering.)
In other words, a negligible amount of utility loss cannot be multiplied so that it is preferable to a concentrated, non-negligible utility loss. If none of the people involved in the negligible-group suffer individually, they obviously can’t be suffering as a group, either (what would be suffering—a group is not an entity!).
However, I have read refutations of this that say “well just replace dust specks with something that does cause suffering.” I have no problem with that; there may be “non-trivial” pain and “non-trivial” pleasure that can be added. So in the stubbed-toes example, it might be non-trivial, since it is concentrated enough to matter to the individual and cause suffering; and suffering is additive.
Perhaps there is such a line innately built into human biology, between “trivial” and “non-trivial”. Eye-motes can’t ever really degrade the quality of our lives, so cannot be used in examples of this kind. But in the case of one person being tortured slightly worse than ten people being tortured slightly less, the non-trivial suffering of the ten can be considered to be additive. This also solves this problem.
What function is that? I thought human utility over money was roughly logarithmic, in which case loss of utility per cent lost would grow until (theoretically) hitting an asymptote. (Also, why would it make sense for it to eventually start falling?)
I thought human utility over money was roughly logarithmic, in which case loss of utility per cent lost would grow until (theoretically) hitting an asymptote.
So you’re saying that being broke is infinite disutility. How seriously have you thought about the realism of this model?
Obviously I didn’t mean that being broke (or anything) is infinite disutility. Am I mistaken that the utility of money is otherwise modeled as logarithmic generally?
It was in response to the “indefinitely” in the parent comment, but I think I was just thinking of the function and not about how to apply it to humans. So actually your original response was pretty much exactly correct. It was a silly thing to say.
I wonder if it’s correct, then, that the marginal disutility (according to whatever preferences are revealed by how people actually act) of the loss of another dollar actually does eventually start decreasing when a person is in enough debt. That seems humanly plausible.
I have no idea what function it is. I also don’t really have a working understanding of what “logarithmic” is. It starts falling because when you’re dealing in the thousands of dollars, the next dollar matters less than it did when you were dealing in the tens of dollars.
Oh, okay, I think we’re talking about the same function in different terms. You’re talking in terms of the utility function itself, and I was talking about how much the growth rate falls as the amount of money decreases from some positive starting point, since that’s what Hul-Gil seemed to be talking about. (I think that would be hyperbolic rather than exponential, though.)
The utility function itself does grow indefinitely; just really slowly at some point. And at no point is its own growth speeding up rather than slowing down.
What’s worse, stealing one cent each from 5,000,000 people, or stealing $49,999 from one person? (Let us further assume that money has some utility value.)
If we decide we can just add the diminished wealth together, the former is clearly one cent worse: $50,000 is stolen, as opposed to $49,999. But this doesn’t take into account that loss of utility grows with each cent lost from the same person. Losing one cent won’t bother me at all; everyone else who had a cent stolen would probably feel the same way. However, $49,999 from one person is enough to ruin their life: numerically, less was stolen overall, but the utility loss grows incredibly as it is concentrated.
Another case: is an eye-mote a second for a year (31,556,926 motes) in one person better than 31,556,927 motes spread out evenly among 31,556,927 people? The former case would involve serious loss of utilons, whereas a single mote is quickly fixed and forgotten: qualitatively different from constant irritation. The loss of utilons from dust motes can thus be concentrated and added, but not spread out and then added. (I think this may indicate time and memory plays a factor in this, since they do in the mechanism of suffering.)
In other words, a negligible amount of utility loss cannot be multiplied so that it is preferable to a concentrated, non-negligible utility loss. If none of the people involved in the negligible-group suffer individually, they obviously can’t be suffering as a group, either (what would be suffering—a group is not an entity!).
However, I have read refutations of this that say “well just replace dust specks with something that does cause suffering.” I have no problem with that; there may be “non-trivial” pain and “non-trivial” pleasure that can be added. So in the stubbed-toes example, it might be non-trivial, since it is concentrated enough to matter to the individual and cause suffering; and suffering is additive.
Perhaps there is such a line innately built into human biology, between “trivial” and “non-trivial”. Eye-motes can’t ever really degrade the quality of our lives, so cannot be used in examples of this kind. But in the case of one person being tortured slightly worse than ten people being tortured slightly less, the non-trivial suffering of the ten can be considered to be additive. This also solves this problem.
On this end of the scale, it grows (I’m not sure if it’s exponential), but it doesn’t grow indefinitely; eventually it starts falling.
A good point. I’ve edited to rephrase.
What function is that? I thought human utility over money was roughly logarithmic, in which case loss of utility per cent lost would grow until (theoretically) hitting an asymptote. (Also, why would it make sense for it to eventually start falling?)
So you’re saying that being broke is infinite disutility. How seriously have you thought about the realism of this model?
Obviously I didn’t mean that being broke (or anything) is infinite disutility. Am I mistaken that the utility of money is otherwise modeled as logarithmic generally?
Then what asymptote were you referring to?
It was in response to the “indefinitely” in the parent comment, but I think I was just thinking of the function and not about how to apply it to humans. So actually your original response was pretty much exactly correct.
It was a silly thing to say.
I wonder if it’s correct, then, that the marginal disutility (according to whatever preferences are revealed by how people actually act) of the loss of another dollar actually does eventually start decreasing when a person is in enough debt. That seems humanly plausible.
I have no idea what function it is. I also don’t really have a working understanding of what “logarithmic” is. It starts falling because when you’re dealing in the thousands of dollars, the next dollar matters less than it did when you were dealing in the tens of dollars.
Oh, okay, I think we’re talking about the same function in different terms. You’re talking in terms of the utility function itself, and I was talking about how much the growth rate falls as the amount of money decreases from some positive starting point, since that’s what Hul-Gil seemed to be talking about. (I think that would be hyperbolic rather than exponential, though.)
The utility function itself does grow indefinitely; just really slowly at some point. And at no point is its own growth speeding up rather than slowing down.