Hi. I think there is an error in the part your analysis dealing with the cost of developing cell-based meat.
Assume in the business as usual scenario (where you do not contribute) the same amount of money is funded (by other people) every year until cell-based meat becomes cost-competitive with animal-based meat on the market. In other words, if 108 euro were not invested in cell-based meat this year, the arrival of cell-based meat on the market would be delayed by one year.
If i understood correctly, we are operating under the simplifying assumption where developing cost-competitive cell-based meat has some up front cost C and then yields U utility every year, forever, starting once that up front cost is paid. If we’re choosing between a bunch of interventions that work the same way, then we should first fund whichever intervention has the highest return on investment, which would be U/C.
In comparing two different interventions that achieve an equally good outcome, we should fund whichever has the lower cost. I don’t think we can get away with not making an actual estimate of the cost required to accomplish the goal. Under the reasoning used in your analysis, where the current level of funding is used as the cost to advance progress by one year, we would instead end up choosing to fund whichever intervention has the lowest current level of funding, even if completing it would cost more than an alternative intervention.
In the scenario where the level of funding F is the same every year, if you make a one time donation x, the outcome gets closer by xF years, therefore you’ve produced U⋅xF utility.
The main assumption behind this result is that some utility U in the future is worth as much as some utility U right now. Therefore, when judging which of two projects is the best, since C only affects how long it will take to complete each project, it doesn’t matter. The only quantities that matter are U of course, and the funding F.
What if you want to take into account the fact that no, some utility in the future is worth less than some utility right now, therefore completing quick projects first is better?
Warning : this part will involve math
One common way to do that is to assume that the utility decreases over time in a geometrical manner : 1 utility unit in 1 year is equivalent to τ utility units now, 1 unit in two years is equal to τ2 utility units now, with τ slightly smaller than 1. For example, if τ is equal to 0.99, then one utility point in one century is worth about one third of one now, and the closer τ is to 1, the more you adopt a longtermist point of view.
Ok so now we can compute the total utility of a project with cost C, annual funding F, and per year utility U :
Utotal=U⋅11−τ⋅τCF
Now, making a one-time donation x, is the same as decreasing the total cost C by x, thus the utility gain of this donation will be :
gain=x⋅−∂Utotal∂C=U⋅−ln(τ)1−τ⋅τCF⋅xF=U⋅τCF⋅xF
So we have three factors : U, of course, xF, which is how many years of funding you’ll provide with your donation, and τCF which represents how much this future utility is worth, compared to utility right now. Once again, if you think that utility in the future is equal to utility now, which means τ=1, you get gain=U⋅xF, which is the original formula in the post. C matters only if utility in the future is not equal to utility in the present.
Now, we can re-write this formula with your notion of return on investment :
gain=x⋅UC⋅CFτCF
With this version, we see three factors influencing the gains : x, the bigger your donation, the better, UC, the bigger the return on investment, the better, and finally CFτCF, which is a function of CF, the number of remaining years. This function is convex, it starts at 0, reaches a maximum, and its limit is 0 again when CF approches infinity.
#TODO : include a graph of this function, once I figure out how to do that
With this model, when CF is too small, it means that the project will soon be funded with or without you, thus you shouldn’t invest in it. On the other extreme, if CF is too big, the benefits will take place too far in the future, and because utility points lose value when too far in the future, you shouldn’t invest in it either. In the middle are the best projects.
Anyway, the main point is : the cost C matters only if you think that utility right now is worth more than utility in the future, otherwise only the funding F matters
In your equation where future benefits are discounted, using the derivative makes sense if your donation is small relative to the total cost of the project. I was doing the opposite and assuming that we pay for the whole thing. Given that the estimated cost is in the billions of dollars and a lot of that funding is from people we can’t coordinate with, your assumption seems closer to reality than mine.
Without discounting, things are less straightforward and i’ve got a messy page of math/notes right now that i’ll try to turn into something post-able this weekend. But basically when i wrote that we should first fund whichever option has higher U/C, i had forgotten the assumptions that that result was based on. U/C is the right metric if there is no outside funding and you have a constant income per year. The way you’re approaching the problem is as if we have a limited budget to use today and no income and each project has a constant, positive amount of outside funding per year. I wrote out a bunch of equations under those assumptions and am convinced that, given two projects, we should choose whichever has higher U/F. At least the way i derived them, these metrics come from calculations that work around the whole infinite utility thing by looking at the difference in the finite amounts of utility that we miss out on (relative to having both projects done at time zero) depending on which of two projects we fund first, so this stuff does not generally result in “utility per dollar” numbers that can be compared to other cost-effectiveness estimates where everything is nice and finite.
If there’s no outside funding and your money is limited, some projects will never be completed, which causes infinity-related issues that break everything. With finite utilities, i think that’s just a knapsack problem.
I have not yet figured out a solution for the case where we have an annual income, there is outside funding, and no discounting, but that’s the plan.
Following up on this, i did work out a solution for the case where we have an annual income, there is outside funding, there’s no discounting, and there’s a consumption option where instead of funding a project we can just collect K utils per dollar. The work behind this is a mess, partly because the equations get long and partly because it was mostly just me doing the same thing repeatedly for slightly different situations until i stopped being confused. Since either declining to show my work or putting 14 kilobytes of garbage in a forum comment would both be bad, here it is in a pastebin link: https://pastebin.com/raw/PnDZ2rTZ
The result is if there are two projects, X and Y, and our income I is such that we can’t affect which of two projects gets done first, that is, if C_X / F_X < C_Y / (F_Y + I), then project X will always be finished before project Y and there’s nothing we can do about it, then we should fund whichever project has higher U/F. But if we are able to affect which project gets done first, we should fund whichever has higher (U—K*F) / C.
And after thinking about it more and writing more equations, i think U/F really does give us a direct comparison of project-like interventions (utility over time forever once it’s fully funded) to consumption-like interventions (utility per dollar). And it gives us a direct comparison of project-like interventions if we can spend money to complete a project in zero time. And it gives us a direct comparison of project-like interventions in the case where making/spending money takes time, but that time doesn’t matter because we can’t change the order in which things get done. The case where it does not work is when we have an annual income as opposed to a one-shot budget and we’re comparing two project-like interventions and the one that we fund first is the one that gets done first.
I think what makes the result for the case where we have an income and can determine which intervention gets done first so qualitatively different from the case where have a stack of cash and can choose between two projects to knock out is that we have to take into account how much choosing to fund the first project delays our ability to fund the second project. And that delay is proportional to C. (Everything here is assuming no diminishing returns to rate of funding, so it’s always best to concentrate funding on one project to knock it out as soon as possible and never makes sense to split funding between projects and get neither one done.)
Thanks! I assumed indeed a zero discount rate, because I believe the disutility of farm animal suffering in the future counts the same as the disutility today. Perhaps one could use a very small discount rate, to account for a human extinction probability, but then again, when humans are extinct, there will be no more farm animal suffering. I guess a higher discount rate matters when utility measures greenhouse gas emisions saved. Reducing 1 ton CO2 now is more important than 1 ton later (because in the future the carbon absorption capacity by forests, oceans and carbon capture and storage technologies will be bigger). However, I think cell-based meat will enter the market within 10 years, so I don’t expect C/F to be very big.
I think cell-based meat will enter the market within 10 years, so I don’t expect C/F to be very big
This makes cell-based meat R&D actually less effective : without discount gain=x⋅UC⋅CF
In term of farm animal suffering, you estimation is U=0.1⋅1011, and C = 1010 . So for each euro invested, you’ll avoid the suffering of CF farm animals. The smaller the time we have to wait before cell-based meat enters the market, the less we should donate.
(This is basically because if cell-based meat enters the market in 10 years, instead of 100, its neglectedness is 10 times smaller, therefore your donation is ten times less effective)
[EDIT]
It actually depends on why you think it will be 10 years instead of 100 : if you think it’s because funding will be bigger, then the neglectedness is smaller. If, instead, you think that’s because the cost is smaller (C = 109), then, as previously stated, it doesn’t impact the effectiveness of the donation
Sorry, I’m not following. The gain is independent of C, and hence (at given U and F) independent of the expected time period. Assume x is such that cell-based meat enters the market 1 year sooner (i.e. x=F). Accelerating cell-based meat with one year is equally good (spares U=0,1.10^11 animals), whether it is a reduction from 10 to 9 years or 100 to 99 years. Only if C/F would be smaller than a year, accelerating with 1 year would not work.
I totally agree with you, the gain is independent of C.
In your original post, you give a scenario where the cell-based meat enters the market in 100 years, while you seem to believe that an actual estimate would rather be ten years or less. I wondered if this was because you overestimated C, or underestimated F (both affect the timeline, but only F affects the gain)
I now understand that you overestimated C, so this doesn’t affect your prediction about the gain
The basic (in my opinion realisitic) assumption is that other people invest in cell-based meat R&D anyway, and that in the business-as-usual scenario (where you do not fund anything) no other strategy (technology, intervention, vegan outreach campaign,...) will be able (even with more funding) to abolish animal farming before cell-based meat enters the market at competitive prices. Suppose cell-based meat arrives within a few decades and eliminates animal farming in say 50 years, whereas another, next best strategy would eliminate animal farming in 100 years. Suppose that this other strategy was less costly, for example requiring only 10 million euro funding per year over a period of 100 years to abolish animal farming, whereas cell-based meat would require 100 million euro funding over 50 years. And suppose that other strategy was more neglected, for example receiving only 10 million euro funding per year, compared to 100 million for cell-based meat. Even then, extra funding for that other strategy would not be effective when it is impossible to speed it up such that it will eliminate animal farming within 50 years. When that other strategy takes more than 50 years anyway, it will become obsolete anyway in the business-as-usual scenario where cell-based meat arrives earlier and eliminates animal farming earlier. A global coordination such that all cell-based meat funding goes to that other, less costly strategy, is not effective (not so feasible). Hence, the most effective thing to do for us, is to accelerate that cell-based meat research, such that it enters the market one year earlier. That saves an extra year of animal suffering and greenhouse gas emissions. If other strategies received more funding, there is a likelihood that they make cell-based meat obsolete, and this consideration is included in the 10% probability of cell-based meat eliminating animal farming.
Gotcha. I was thinking about a much simpler situation where we’re comparing two interventions to accomplish equally valuable goals, rather than two interventions to accomplish the same goal, where finishing one makes the other obsolete. I was also assuming that we are able to coordinate on what to fund. But in the situation you described, it makes sense to fund the cheaper intervention only if we can put together enough money for it to overtake the one that’s already being funded, like 555,555,555 euros in your example. But that number is assuming we can just linearly spend money to make stuff happen sooner.
If your belief that
no other strategy (technology, intervention, vegan outreach campaign,...) will be able (even with more funding) to abolish animal farming before cell-based meat enters the market at competitive prices
is true, then it makes sense that people funding other strategies to abolish animal farming should coordinate to instead fund cell based meat. (Unless those other strategies also produce a significant amount of utility in the short term that falls short of abolition.) I don’t know nearly enough about this stuff to evaluate your claim that cell based meat will probably be the thing that ends animal farming, but it seems like something that’s important if it’s true, and i think you should post your reasons for believing this as a new top level forum post.
Hi. I think there is an error in the part your analysis dealing with the cost of developing cell-based meat.
If i understood correctly, we are operating under the simplifying assumption where developing cost-competitive cell-based meat has some up front cost C and then yields U utility every year, forever, starting once that up front cost is paid. If we’re choosing between a bunch of interventions that work the same way, then we should first fund whichever intervention has the highest return on investment, which would be U/C.
In comparing two different interventions that achieve an equally good outcome, we should fund whichever has the lower cost. I don’t think we can get away with not making an actual estimate of the cost required to accomplish the goal. Under the reasoning used in your analysis, where the current level of funding is used as the cost to advance progress by one year, we would instead end up choosing to fund whichever intervention has the lowest current level of funding, even if completing it would cost more than an alternative intervention.
In the scenario where the level of funding F is the same every year, if you make a one time donation x, the outcome gets closer by xF years, therefore you’ve produced U⋅xF utility.
The main assumption behind this result is that some utility U in the future is worth as much as some utility U right now. Therefore, when judging which of two projects is the best, since C only affects how long it will take to complete each project, it doesn’t matter. The only quantities that matter are U of course, and the funding F.
What if you want to take into account the fact that no, some utility in the future is worth less than some utility right now, therefore completing quick projects first is better?
Warning : this part will involve math
One common way to do that is to assume that the utility decreases over time in a geometrical manner : 1 utility unit in 1 year is equivalent to τ utility units now, 1 unit in two years is equal to τ2 utility units now, with τ slightly smaller than 1. For example, if τ is equal to 0.99, then one utility point in one century is worth about one third of one now, and the closer τ is to 1, the more you adopt a longtermist point of view.
Ok so now we can compute the total utility of a project with cost C, annual funding F, and per year utility U :
Utotal=U⋅11−τ⋅τCF
Now, making a one-time donation x, is the same as decreasing the total cost C by x, thus the utility gain of this donation will be :
gain=x⋅−∂Utotal∂C=U⋅−ln(τ)1−τ⋅τCF⋅xF=U⋅τCF⋅xF
So we have three factors : U, of course, xF, which is how many years of funding you’ll provide with your donation, and τCF which represents how much this future utility is worth, compared to utility right now. Once again, if you think that utility in the future is equal to utility now, which means τ=1, you get gain=U⋅xF, which is the original formula in the post. C matters only if utility in the future is not equal to utility in the present.
Now, we can re-write this formula with your notion of return on investment :
gain=x⋅UC⋅CFτCF
With this version, we see three factors influencing the gains : x, the bigger your donation, the better, UC, the bigger the return on investment, the better, and finally CFτCF, which is a function of CF, the number of remaining years. This function is convex, it starts at 0, reaches a maximum, and its limit is 0 again when CF approches infinity.
#TODO : include a graph of this function, once I figure out how to do that
With this model, when CF is too small, it means that the project will soon be funded with or without you, thus you shouldn’t invest in it. On the other extreme, if CF is too big, the benefits will take place too far in the future, and because utility points lose value when too far in the future, you shouldn’t invest in it either. In the middle are the best projects.
Anyway, the main point is : the cost C matters only if you think that utility right now is worth more than utility in the future, otherwise only the funding F matters
In your equation where future benefits are discounted, using the derivative makes sense if your donation is small relative to the total cost of the project. I was doing the opposite and assuming that we pay for the whole thing. Given that the estimated cost is in the billions of dollars and a lot of that funding is from people we can’t coordinate with, your assumption seems closer to reality than mine.
Without discounting, things are less straightforward and i’ve got a messy page of math/notes right now that i’ll try to turn into something post-able this weekend. But basically when i wrote that we should first fund whichever option has higher U/C, i had forgotten the assumptions that that result was based on. U/C is the right metric if there is no outside funding and you have a constant income per year. The way you’re approaching the problem is as if we have a limited budget to use today and no income and each project has a constant, positive amount of outside funding per year. I wrote out a bunch of equations under those assumptions and am convinced that, given two projects, we should choose whichever has higher U/F. At least the way i derived them, these metrics come from calculations that work around the whole infinite utility thing by looking at the difference in the finite amounts of utility that we miss out on (relative to having both projects done at time zero) depending on which of two projects we fund first, so this stuff does not generally result in “utility per dollar” numbers that can be compared to other cost-effectiveness estimates where everything is nice and finite.
If there’s no outside funding and your money is limited, some projects will never be completed, which causes infinity-related issues that break everything. With finite utilities, i think that’s just a knapsack problem.
I have not yet figured out a solution for the case where we have an annual income, there is outside funding, and no discounting, but that’s the plan.
Following up on this, i did work out a solution for the case where we have an annual income, there is outside funding, there’s no discounting, and there’s a consumption option where instead of funding a project we can just collect K utils per dollar. The work behind this is a mess, partly because the equations get long and partly because it was mostly just me doing the same thing repeatedly for slightly different situations until i stopped being confused. Since either declining to show my work or putting 14 kilobytes of garbage in a forum comment would both be bad, here it is in a pastebin link: https://pastebin.com/raw/PnDZ2rTZ
The result is if there are two projects, X and Y, and our income I is such that we can’t affect which of two projects gets done first, that is, if C_X / F_X < C_Y / (F_Y + I), then project X will always be finished before project Y and there’s nothing we can do about it, then we should fund whichever project has higher U/F. But if we are able to affect which project gets done first, we should fund whichever has higher (U—K*F) / C.
And after thinking about it more and writing more equations, i think U/F really does give us a direct comparison of project-like interventions (utility over time forever once it’s fully funded) to consumption-like interventions (utility per dollar). And it gives us a direct comparison of project-like interventions if we can spend money to complete a project in zero time. And it gives us a direct comparison of project-like interventions in the case where making/spending money takes time, but that time doesn’t matter because we can’t change the order in which things get done. The case where it does not work is when we have an annual income as opposed to a one-shot budget and we’re comparing two project-like interventions and the one that we fund first is the one that gets done first.
I think what makes the result for the case where we have an income and can determine which intervention gets done first so qualitatively different from the case where have a stack of cash and can choose between two projects to knock out is that we have to take into account how much choosing to fund the first project delays our ability to fund the second project. And that delay is proportional to C. (Everything here is assuming no diminishing returns to rate of funding, so it’s always best to concentrate funding on one project to knock it out as soon as possible and never makes sense to split funding between projects and get neither one done.)
Thanks! I assumed indeed a zero discount rate, because I believe the disutility of farm animal suffering in the future counts the same as the disutility today. Perhaps one could use a very small discount rate, to account for a human extinction probability, but then again, when humans are extinct, there will be no more farm animal suffering. I guess a higher discount rate matters when utility measures greenhouse gas emisions saved. Reducing 1 ton CO2 now is more important than 1 ton later (because in the future the carbon absorption capacity by forests, oceans and carbon capture and storage technologies will be bigger). However, I think cell-based meat will enter the market within 10 years, so I don’t expect C/F to be very big.
Thanks for your response!
This makes cell-based meat R&D actually less effective : without discount gain=x⋅UC⋅CF
In term of farm animal suffering, you estimation is U=0.1⋅1011, and C = 1010 . So for each euro invested, you’ll avoid the suffering of CF farm animals. The smaller the time we have to wait before cell-based meat enters the market, the less we should donate.
(This is basically because if cell-based meat enters the market in 10 years, instead of 100, its neglectedness is 10 times smaller, therefore your donation is ten times less effective)
[EDIT]
It actually depends on why you think it will be 10 years instead of 100 : if you think it’s because funding will be bigger, then the neglectedness is smaller. If, instead, you think that’s because the cost is smaller (C = 109), then, as previously stated, it doesn’t impact the effectiveness of the donation
Sorry, I’m not following. The gain is independent of C, and hence (at given U and F) independent of the expected time period. Assume x is such that cell-based meat enters the market 1 year sooner (i.e. x=F). Accelerating cell-based meat with one year is equally good (spares U=0,1.10^11 animals), whether it is a reduction from 10 to 9 years or 100 to 99 years. Only if C/F would be smaller than a year, accelerating with 1 year would not work.
I totally agree with you, the gain is independent of C.
In your original post, you give a scenario where the cell-based meat enters the market in 100 years, while you seem to believe that an actual estimate would rather be ten years or less. I wondered if this was because you overestimated C, or underestimated F (both affect the timeline, but only F affects the gain)
I now understand that you overestimated C, so this doesn’t affect your prediction about the gain
Thanks for clarifying!
The basic (in my opinion realisitic) assumption is that other people invest in cell-based meat R&D anyway, and that in the business-as-usual scenario (where you do not fund anything) no other strategy (technology, intervention, vegan outreach campaign,...) will be able (even with more funding) to abolish animal farming before cell-based meat enters the market at competitive prices. Suppose cell-based meat arrives within a few decades and eliminates animal farming in say 50 years, whereas another, next best strategy would eliminate animal farming in 100 years. Suppose that this other strategy was less costly, for example requiring only 10 million euro funding per year over a period of 100 years to abolish animal farming, whereas cell-based meat would require 100 million euro funding over 50 years. And suppose that other strategy was more neglected, for example receiving only 10 million euro funding per year, compared to 100 million for cell-based meat. Even then, extra funding for that other strategy would not be effective when it is impossible to speed it up such that it will eliminate animal farming within 50 years. When that other strategy takes more than 50 years anyway, it will become obsolete anyway in the business-as-usual scenario where cell-based meat arrives earlier and eliminates animal farming earlier. A global coordination such that all cell-based meat funding goes to that other, less costly strategy, is not effective (not so feasible). Hence, the most effective thing to do for us, is to accelerate that cell-based meat research, such that it enters the market one year earlier. That saves an extra year of animal suffering and greenhouse gas emissions. If other strategies received more funding, there is a likelihood that they make cell-based meat obsolete, and this consideration is included in the 10% probability of cell-based meat eliminating animal farming.
Gotcha. I was thinking about a much simpler situation where we’re comparing two interventions to accomplish equally valuable goals, rather than two interventions to accomplish the same goal, where finishing one makes the other obsolete. I was also assuming that we are able to coordinate on what to fund. But in the situation you described, it makes sense to fund the cheaper intervention only if we can put together enough money for it to overtake the one that’s already being funded, like 555,555,555 euros in your example. But that number is assuming we can just linearly spend money to make stuff happen sooner.
If your belief that
is true, then it makes sense that people funding other strategies to abolish animal farming should coordinate to instead fund cell based meat. (Unless those other strategies also produce a significant amount of utility in the short term that falls short of abolition.) I don’t know nearly enough about this stuff to evaluate your claim that cell based meat will probably be the thing that ends animal farming, but it seems like something that’s important if it’s true, and i think you should post your reasons for believing this as a new top level forum post.