The chart above shows 2 possible worlds: A and Z. In A, everyone has really awesome lives. In Z, everyone has lives that are barely worth living, but there are way way more people in existence. Which is better? Most everyone, including myself, would agree that A is better.
Now consider the possible worlds shown above, represented in the same way as the first picture. How does A compare to A+? A+ takes the same people with the same quality of life as in A, and adds another equally-sized group of people with a lesser but still enjoyable quality of life. For simplicity, assume that the 2 groups of people are completely isolated and have no effect on each other. How would you compare those 2 worlds? Most everyone, including myself, would find it obvious that, at the very least, A+ is not worse than A. Merely adding people with enjoyable lives, as long as they don't reduce the quality of the previously existing people's lives, surely cannot be a bad thing.
What about comparing A+ and B? They both have the same number of people. Quality of life for those people is much higher than the lesser group in A+ but only slightly lower than the higher group in A+. So the average life is better than in A+. Most of us, including myself, would say that B is a better world than A+.
So we've decided that A > Z, A+ >= A, and B > A+. Do you see the problem? If B > A+ and A+ is not worse than A, that logically means that B > A. And if you keep increasing the population and rebalancing from B, the same way you moved from A to B, you can get to Z... where there are a whole lot of people with lives barely worth living. We intuitively feel that Z is worse than A. But our intuitions on some other scenarios imply the opposite. So we have a contradiction. Which of our intuitions are incorrect?
It may be simpler to imagine, and with similarly disturbing results, to apply this same line of thought to 1 person's life, where expanding horizontally in the graphs above is adding more years to their life rather than adding more people.
I used to think utilitarianism, while difficult in practice, was extremely simple in theory. I guess not.