Imagine the discovery of a new type of chair. This chair would produce great happiness and wellbeing to those sitting in it. As we live in a world with limited resources, suppose we would only be able to produce one hundred such chairs. Suppose also that the chair would have to be produced in such a way that sharing the chairs will not work (for example, the production of happiness requires genetically coding the chairs). However, the method of distribution of the chair is undetermined: could be a lottery, could be money, could be only for heads of state etc. That’s not important in the present context. Now, imagine also that a greater total of wellbeing (call it utility if you must) could be produced with the same investment, and by giving each and every individual a very, very small increase in his or her personal wellbeing. For example, we could use the money in order to fit all chairs in the world with a massage function. In total, all these small improvements in wellbeing would produce more total wellbeing than just providing one hundred individuals with great happiness by way of the newly invented happiness chairs.
A similar dilemma was featured here.