First I want to thank everyone for the critical examination of (traditional, classical) utilitarianism and negative utilitarianism and all the interesting points made thereof.
Be sure that whenever you are describing utilitarianism, that you present it as moral, &/or ethical. Classical, traditional utilitarianism is a consequentialist moral theory that is concerning with maximizing the happiness and pleasure for the most amount of people. The actions that produce the consequences are not moral in-and-of-themselves, therefore the happiness of the consequences are where the morality is empirically determined. That is not to suggest that the actions or the consequences are im/moral in-and-of-themselves. Although outside of the theory this might appear to be the case. For example, the “trolley problem” is meant to illustrate this point. If we let the trolley hit one person to save five people, then our action is still morally sound on utilitarian grounds. Yet we are inclined to think that the action is not morally sound, given that you still have to decide to let the trolley kill one person and this does not seem to be moral—hence it is a problem with utilitarianism.
Concerning the notion that the two moral theories are contradictory, or opposites, or something like that. Let’s see how the two are not contradictory. Right away we see that both theories are moral. The two theories are consequential. The two theories are also aimed at helping the most amount of people. As we noticed the two theories seem to complement each other. Whereby we posited that to increase happiness appears to be the same as reducing pain. Yet, we have to ask if it is the same to promote happiness over reducing pain. If I insist that the consequences of an action to increase the happiness of others rests on their pleasure, the pleasure of the majority might un/intentionally bring about the pain of the minority. We cannot make everyone happy, but we can try to make the most happy and making the most happy possibly decreases the happiness of others. For example, racism might want to appeal to the idea that one racial group is a majority, and to appease the majority is best while at the same time having the consequence of making others increasingly unhappy.
Another difference, of course rests on how each theory “helps”. With traditional utilitarianism we seek to help by increasing the happiness (or pleasure) for the most amount of people (to determine the rightness or wrongness of a specific consequence). Then with Popper’s negative utilitarianism we seek to help by reducing suffering (or pain) for the most amount of people (to determine the rightness or wrongness of a specific consequence).
Although I am tempted to agree that the two appear to extend into each other with the notion that to increase happiness implies the reduction of pain. I think the way to distinguish the two theories has to rest on the notion that one demands pleasure and happiness while the other does not. If on the battlefield a medic insists that she wants to bring happiness to the injured seems to be a misdirection of bringing no harm (her Hippocratic Oath) and seeking to relieve pain. Pain management does not necessarily bring happiness or even pleasure, but it does help to palliate pain as soon as possible, over and beyond a concern for happiness on the battlefield.
Perhaps the recent “Black Lives Matter” issue is another example of how negative utilitarianism is a useful position. In other words, the movement started in 2013 with the shooting death of Trayvon Martin, extending into the protest and national discussion on the wrongful killing of black people (usually black men) by white law enforcement. Here we can easily see that the objective of the movement is not necessarily happiness, rather the objective is to call into question racial profiling and the killing of innocent black men. Both of these objectives are aimed at the reduction of suffering and the reduction of pain. In other words, happiness and pleasure are only potential byproducts of the aims. Yes, we will be happy if this type of racist killing is done away with. However, I argue that we attack the problem negatively, we wish to do away with the racist killings and profiling to begin with. We attack the problem on negative utilitarian grounds, we aim to reduce the suffering of black men at the hands of white police officers.
Do not get me wrong, I am not trying to suggest that classical utilitarianism is inherently flawed. No, that is not the message, rather I wish to bring in an alternative view to demonstrate that to insist on happiness is not always as beneficial or as realistic as we might imagine.