Population Utilitarianism

[Nick]

Hey, why don't we determine the Utilitiarianism of stem cell research?
Assuming that killing can be balanced out by creating.
Assuming that by creating an embryo you are creating a life.

We get x embryos per day. There are three options: we can discard these embryos, use them to fight disease, or nurture them into human beings. Embryos survive for d days before they must be discarded.

Assuming we simply discard them:
So, for the first d days, we get d * x embryos, giving us a utility of d * x. The number of days c is from when embryos start being discarded to today. After d days, we are discarding x embryos and gaining x embryos per day.

We now have a utiliity of U=dx + (-cx + cx), or U=dx, which is positive.

Assuming we use them to fight disease:

We get x embryos per day, and each day x embryos are used to save y patients.

The Utility is: U=x - x + y or U=y, which is positive.

Assuming we nurture them into society as humans:
We get x embryos per day.

The Utility is U=x.

Now what about Population? If it gets too high, we have social darwinism, which is bad for a society. Let p be the number of people on the earth yesterday (so the embryos nurtured today do not count), and let L (capitalized for clarity) be the limit the earth can hold before peole begin to starve. The equation for nurturing them into humans changes:

The utility of nurturing the embryos you got today is U=x + (L - (p + x)), which has the potential to become negative, but is currently positive..

The equation for discarding does not change for obvious reasons. The equation for stem cell research does not change because the patients being rescued are already part of society; letting him die might even bring down utility.

Tell me your thoughts!

moonlord: Split from "utilitarianism". This will surely be a looong thread.

[PWrong]

Assuming that killing can be balanced out by creating.
Assuming that by creating an embryo you are creating a life.

Technically, life has no inherent value under utilitarianism. It's about minimising suffering and maximising happiness, and embryo's can't feel pain or pleasure. Creating an embryo (in a test tube, not the usual way) does however cost money, which is strongly related to utility.

So, for the first d days, we get d * x embryos, giving us a utility of d * x

Keeping an embryo alive doesn't increase utility, unless you can prove that live embryos are happier than dead embyros. Stem cell research is one of the easiest things to justify with utilitarianism.

Note that in the good/bad AI thread, we equate life to utility because we're considering hypothetical beings who are always happy, as long as they don't get murdered or executed.

Now what about Population? If it gets too high, we have social darwinism, which is bad for a society. Let p be the number of people on the earth yesterday (so the embryos nurtured today do not count), and let L (capitalized for clarity) be the limit the earth can hold before peole begin to starve. The equation for nurturing them into humans changes:

You may be onto something more important than embryos with the population idea . We could take the logistic equation (population growth with a restriction), and find an equation for utility as a function of population and the remaining resources, then try to maximise utility with respect to birth rate. This would tell us the optimal number of children for the average person to have . Of course, we'd have to assume that resources are distributed equally, which they obviously aren't. Still, it could be interesting.

[Nick]

So, for the first d days, we get d * x embryos, giving us a utility of d * x

Keeping an embryo alive doesn't increase utility, unless you can prove that live embryos are happier than dead embyros. Stem cell research is one of the easiest things to justify with utilitarianism.

Yes, keeping an embryo alive doesn't increase utility. But each day your getting x embryos.

As for population, I have no idea how we could do that, but here are some variable we could use:

L = limit of people on earth
p = the number of pairs of women & men
r = the number of kids each 'p' can have
t = remainder of population
t₁ = (p * 2) + t, total population

We might also have to, at first, assume that the lifespan of each individual is the same and that everyone reproduces at the same time; then add those as variable later.

[moonlord]

You may be onto something more important than embryos with the population idea . We could take the logistic equation (population growth with a restriction), and find an equation for utility as a function of population and the remaining resources, then try to maximise utility with respect to birth rate. This would tell us the optimal number of children for the average person to have . Of course, we'd have to assume that resources are distributed equally, which they obviously aren't. Still, it could be interesting.

Let's start with the beginning. [I hope this won't render the "Good AI, bad AI thread dead.]

There are mainly four steps a population will go through. First is the adaptation step, when the population is stable (mortality and natality are equal). Then is the Fibonacci series growth, which is oftenly aproximated with the exponential function. At a certain point, step three starts, when the population is again stable, and is the maximum population the resources can support. After a while, population will decrease, as the resources start being short. If the resources constantly regenerate, when the population is small enough, mortality will again be equal with natality. If not, the population will eventually die.

[PWrong]

Then is the Fibonacci series growth, which is oftenly aproximated with the exponential function.

I don't know if the fibonacci series can be approximated by e^x, but the usual equation for restricted population growth is the logistic equation.

dP/dt = k ( 1 - P/K)
where:
P is population
dP/dt is the rate of change of population
k is the natural population growth (each person has k children per year on average),
K is the maximum population capacity.

You can see that when P=K, the population stops growing. It's possible to solve this differential equation, but it looks better unsolved.

If the average person needs 'r' of some resource, and the total amount of the resource is R, then K = R/r.
We can approximate the average utility as the amount of resources per person, U = R/P. Since P can't go higher than K, it follows that U>r i.e. everyone gets more than they need.

We want to maximise the integral of U over t, by changing k. I'll have a look at this problem tonight. I hope it all made sense.

[PWrong]

Actually, we don't really need the logistic equation at all. Lets just find the best possible population.

The utility of a single person should be some function of the amount of resources per person, that is, R/P.
So we have U = P f(R/P)

We'll say that when we run out of resources, everyone has a utility of U_min. This minimum utility will be negative.
The maximum amount of resources one person can have is R (which happens if P = 1), so let f(R) = U_max.

I've figured out this possible function for f:
f(x) = (U_max - U_min) (1 - e^(-x))/ (1 - e^(-R))
Note that this satisfies f(0) = U_min, f(R) = U_max. It's simpler than it looks, because it's just a constant * (1-e^(-x))

Now we just have to maximise U with respect to P. The graph of U shows that there is a maximum, but there's no formula for it.

Example: For R = 100, U_max = 1, U_min = -1, the solution is about P = 60.

[PWrong]

Sorry for posting three times in a row, but I think I can make this simpler and more general. Rather than actually finding the ideal population, it's sufficient to show that there is an ideal population. I think I can do this using the something like the intermediate value theorem. The same argument will show that there is an ideal number of children to have. This sounds useless, but it defeats a major criticism of utilitarianism. Some people claim that we would be better off overall if the earth simply disappeared, others might think that utilitarianism implies we should all have as many kids as possible. So this theorem would fix that problem.