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Utilitarianism tries to overcome the problems of using egoism as a moral guide by making the basis for decision making what will produce the greatest amount of pleasure for the greatest amount of people. This is obviously in contrast to egoism, which would take the basis for decision making as that which would serve one's own interest and provide for one's pleasure.
The differences between rule and act utilitarianism are as follows: the act utilitarian only considers the results or consequences of a single action whereas the rule utilitarian considers the consequences that result of following a rule of conduct.
Let's take a simple example to make this clearer. You are sitting in an exam, and you realise that you have revised the wrong questions. HELP! But, then you realise that you have left your revision notes in your pocket, so you have the choice of sneaking them out and cheating in your exam.
If you ascribed to Act Utilitarianism, you would look at the consequences of that single action. You would say that cheating would produce the most happiness for you and for your family, as you would get a good grade which would allow you to go to a good college and get a good job etc. By calculating the outcome of this single action, you would think it was worthwhile. So you would cheat!
If you ascribed to Rule Utilitarianism, you would need to consider what the long term consequences would be if everyone cheated in their exams. You would think that if everyone cheated, you would have doctors, lawyers, teachers who weren't able to do their jobs properly, resulting in chaos and a break down in trust in society, as people wouldn't trust that their doctors knew how to heal them. So by calculating the eventual outcome, you would decide that there would be far more harm in cheating in the long run, and you would fail your exam.
Someone goes to the doctor. The person is ill, experiences pain and dysfunction. The doctor performs a series of test and examinations. The person returns to the doctor's office to learn of the results, the diagnosis and prognosis. The doctor is aware that the tests all show that the person has a disease that is incurable and life threatening. In fact even under the most aggressive treatment option there is a survival rate of less than 15% for two years. The doctor is considering what would be GOOD to tell the person. Should the person know the truth or should the person be told something other than the truth? Which is better? Which is the right thing to do? What would be GOOD to do? The act utilitarian might calculate that in telling the truth there will be a great deal of pain and hardly any pleasure at all The person will be upset, their family will be upset, the doctor will be upset in informing the ill person that there is nothing that the doctor can do to alter their condition. The doctor's staff will be upset seeing the person come in for whatever treatment there may be. On the other hand if the doctor makes up a story concerning the diagnosis and prognosis that is not true but that gives the ill person more time to enjoy life before the illness makes it obvious that the end is near, well then the results are different. The doctor is not so upset in seeing the person, the doctor's staff is not upset . The family and friends of the person have some more time with that person to enjoy things instead of being morose and depressed. So the ACT utilitarian might calculate that the GOOD is to lie. The rule utilitarian would need to consider what would the long term consequences be if doctors were to lie to those who come to them and have life threatening, incurable illnesses. The rule utilitarian might calculate that people would no longer be able to trust their doctors and this would break down the confidence they need for their therapies to be effective. The RULE utilitarian might calculate that there is far more harm in lying and so the GOOD is to tell the truth
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