The fallacy of composition is the following: X is good for me, therefore it would be good if X happened for everyone. Or X is good for everyone, therefore X will be good for me.

''The second example is not actually a fallacy, of course. The premise may be false, but the logic is sound.''

 Would that depend upon whether 'everyone' is used in the collective sense (the group) or meaning 'every individual'?

An example of this is the invention of computers. It was not good for individuals, specifically individuals who made type writers. 

or

I win the lottery, that is good, everyone should win the lottery. Incorrect, if everyone won the lottery, the pay-out would be pennies.

''Why is it called CompositionFallacy? I call it TotalizationFallacy. And isn't this a specialization of OverSimplification?''

Most fallacies are specializations of oversimplification. And it's called the composition fallacy because its formulation is actually "a property of a substance is also a property of the composite that includes that substance". As in, hydrogen and oxygen are both gases, therefore H2O must be a gas. Or this one that I've actually seen defended; a relationship governed solely and principally by pure power is evil, hence a relationship governed principally by justice and backed by power is also evil. What you call totalization is just a special case of composition.

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One of the FallaciousArgument''''''s.
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See Also: PersonalChoiceElevatedToMoralImperative