The Principle of Maximum Utility is the idea that one should attempt to maximize total utility for all beings, or at least some weighted average of all beings.
Usually people weigh themselves heavier, but altruistic people would have all humans weigh the same. Really silly animal lovers would even allow animals a nonzero weight.
Some think that the quickest way to maximum utility is for everyone to be really selfish, so we evolve quicker.
When evaluating utility, you mustn't forget to include emotional states. So for example, killing one person to save two would save a life, but it would also create such a huge fear all throughout society that it wouldn't be worth it. If this utilitarian government tried to do it secretly, to avoid scaring everyone, it would just make the consequences worse if they were discovered.

Utilitarianism prescribes The Principle of Utility (or The Greatest Happiness Principle) to determiine the morality of one's actions. The problem with this type of moral cost/benefit analysis is that an individual tends to weigh his or her happiness higher than another's pain. Indeed, it is quite possible to justify immoral actions under the guise of promoting the greater good. Social Darwinism tends demonstrate The Real Principle of Maximum Utility quite well.

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