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Belief is the psychological state in which an individual holds a proposition or premise to be true.
http://en.wikipedia.org/wiki/Belief
Preference (also called "taste" or "penchant") is a concept, used in the social sciences, particularly economics. It assumes a real or imagined "choice" between alternatives and the possibility of rank ordering of these alternatives, based on happiness, satisfaction, gratification, enjoyment, utility they provide. More generally, it can be seen as a source of motivation. In cognitive sciences, individual preferences enable choice of objectives/goals.
http://en.wikipedia.org/wiki/Preference
There is a huge difference, between those, and please re read my post. I never said Belief.