One way to deal with this problem is to ask why do we use the arithmetic sum to calculate the total happiness?. There are plenty of ways this can go. Say, if you believe that two very happy people are better than four half as happy people, then you can define this sum function as sum(happiness_per_person) / number_of_people. Of course, this isn't the only way.
Utilitarianism opens a lot of questions about comparability of utility (or happiness) of different people as well as summation. Is it a totally ordered set? Is it a partially ordered set? Perhaps utility is incomparable (that'd be sad and kind of defeat the whole doctrine, but still).
Also, can unhappiness be compensated by happiness? We unthinkingly rush to treat unhappiness as we would negative numbers and try to sum that with happiness, but what if it doesn't work? What if the person who has no happiness or unhappiness isn't in the same place as the person who is equally happy and unhappy (their dog died, but they found a million $ on the same day)?
A more typical classroom question would be about chopping up a healthy person for organs to fix X unhealthy people -- is there a number of unhealthy people which would justify killing a healthy person for spare parts?
Utilitarianism opens a lot of questions about comparability of utility (or happiness) of different people as well as summation. Is it a totally ordered set? Is it a partially ordered set? Perhaps utility is incomparable (that'd be sad and kind of defeat the whole doctrine, but still).
Also, can unhappiness be compensated by happiness? We unthinkingly rush to treat unhappiness as we would negative numbers and try to sum that with happiness, but what if it doesn't work? What if the person who has no happiness or unhappiness isn't in the same place as the person who is equally happy and unhappy (their dog died, but they found a million $ on the same day)?
A more typical classroom question would be about chopping up a healthy person for organs to fix X unhealthy people -- is there a number of unhealthy people which would justify killing a healthy person for spare parts?