The following excerpt from Wikipedia may not help, it's complicated. But you should at least look at it to get a feel for just how complicated the whole system is. Because that's going to be one of my main points and talking about.
The felicific calculus is an algorithm formulated by utilitarian philosopher Jeremy Bentham for calculating the degree or amount of pleasure that a specific action is likely to cause. Bentham, an ethical hedonist, believed the moral rightness or wrongness of an action to be a function of the amount of pleasure or pain that it produced. The felicific calculus could, in principle at least, determine the moral status of any considered act. The algorithm is also known as the utility calculus, the hedonistic calculus and the hedonic calculus.
Variables, or vectors, of the pleasures and pains included in this calculation, which Bentham called "elements" or "dimensions", were:[clarification needed]
Intensity: How strong is the pleasure?
Duration: How long will the pleasure last?
Certainty or uncertainty: How likely or unlikely is it that the pleasure will occur?
Propinquity or remoteness: How soon will the pleasure occur?
Fecundity: The probability that the action will be followed by sensations of the same kind.
Purity: The probability that it will not be followed by sensations of the opposite kind.
Extent: How many people will be affected?
End wiki quote.
You think that sounds bad? Buckle your seatbelt! That's just the first step!
If you want to know the remaining steps, look at the bottom of the of this post for all the rest.
To sum that up, basically, Jeremy Bentham believed in hedonistic ethics. That means if it makes people feel good then it's good. He thought he could make this all very scientific. If you started by just answering the questions above then you would begin to have an idea of how many people would be made to feel good versus how many people would be made to feel bad by a certain action.
The first problem with this is been pointed out many times in the past; what if it makes people feel good to burn a few witches? According to Bentham's ideas, if burning three witches makes 8 million people feel good then we should burn the witches. They'll suffer terrible pain. But 8 million people will be very happy. Bentham was very clever, but he just didn't think things through very carefully. Let me correct that. He thought things through very carefully, he just didn't think very clearly. He got so wrapped up in his bright idea, he forgot that it had to be applied in the real world where things get really messy. Yeah I know, I'm saying things get messy in the real world again. But that's the problem with most philosophers, they forget that.
It's the teacher in me. They just can't seem to get the lesson right, so I'll keep repeating it until they do.
Okay back to his calculus. The first problem, then, is that it says that feeling good is the only value. There are other values than that. Sometimes we do things that make us feel bad, because it's the right thing to do. Now we're getting back into the argument about egoism and if you want to go back to that, look at the earlier posts.
The second problem is that the whole thing is subjective. How can you possibly tell how much pleasure one person is feeling compared to the pleasure of another person is feeling? How could you compare the level of suffering one person is feeling compared to the level of suffering another person is feeling?
We can measure how many calories a person ate today. We can measure how tall a person is. We can measure how many hours of sleep they get. But there's simply no way to compare happiness and suffering from person-to-person. It's all subjective. What one person feels can only be known to that one person. The rest of us can make a pretty good guess, but it's not accurate or factual.
That means of his entire carefully constructed system is totally impossible to apply. It simply cannot be done.
So there are two fatal flaws. One, simply feeling good is not a good basis for deciding what is moral or immoral. Two, how can you compare one person's good feelings or bad feelings to another person's good feelings or bad feelings with any accuracy? You can't. Even Bentham admitted this in his calculations because he keeps referring to that which "appears" to be so. That's just a flat out admission that all of this is nothing but guesswork, nothing scientific about it.
It's hard to find anything good in the system. Since the system is impossible to ever actually apply, how could there be anything good about it? You might just as well ask, what is good or bad about using fairies to grant your wishes? Too silly?
Okay. Here's an actual case. A few years ago, a nuclear engineer in Egypt solved all the worlds future energy problems. At least he thought he had. Remember, we're not talking Homer Simpson. Were talking an actual, post-doctorate scientist. He was also a fundamentalist believer in Islam. The Koran says that there are genies. Therefore he concluded they must exist. He went on to decide that if we could just capture a few genies they would provide an endless source of free energy which would cost nothing and have no environmental impacts.
Debating the value of his idea is pointless. Genies don't exist.
The only benefit of Bentham's system is that you could give yourself some kind of comfort by going to all the elaborate trouble of making his calculations and then tell yourself that it was a scientific conclusion. There might be some value in that, but the value is delusional.
Sorry, Kid, but I just can't say anything good about Bentham's system. Although, as a teacher, I suppose I could say A for effort!
THE REST OF THE STEPS: Warning: even looking at this makes my head hurt.
Of the value of each pain which appears to be produced by it in the first instance.
Of the value of each pleasure which appears to be produced by it after the first. This constitutes the fecundity of the first pleasure and the impurity of the first pain.
Of the value of each pain which appears to be produced by it after the first. This constitutes the fecundity of the first pain, and the impurity of the first pleasure.
Sum up all the values of all the pleasures on the one side, and those of all the pains on the other. The balance, if it be on the side of pleasure, will give the good tendency of the act upon the whole, with respect to the interests of that individual person; if on the side of pain, the bad tendency of it upon the whole.
Take an account of the number of persons whose interests appear to be concerned; and repeat the above process with respect to each. Sum up the numbers expressive of the degrees of good tendency, which the act has, with respect to each individual, in regard to whom the tendency of it is good upon the whole. Do this again with respect to each individual, in regard to whom the tendency of it is bad upon the whole. Take the balance which if on the side of pleasure, will give the general good tendency of the act, with respect to the total number or community of individuals concerned; if on the side of pain, the general evil tendency, with respect to the same community.