There is a reason why I used 'rule', and in turn, 'exception'.
The majority vs minority dichotomy speaks about quantity, and doesn't offer an elucidation of the context.
I am not so complex lah, I treat it as a face value question when you ask why are there people that don't support the victors.
I suppose it's each individual value system.

Here's are some studies...
http://www.sciencedaily.com/releases/2007/12/071219155445.htm
ScienceDaily (Dec. 20, 2007) — In a series of studies, researchers from the University of South Florida tested the scope of people's support for those who are expected to lose, seeking to understand why people are drawn to the Rocky Balboas and the Davids (versus Goliaths) of the world.
Why do people support underdogs and find them so appealing?
The researchers propose that those who are viewed as disadvantaged arouse people's sense of fairness and justice -- important principles to most people
http://lesswrong.com/lw/7s/why_support_the_underdog/
One of the strangest human biases is the almost universal tendency to support the underdog.
I say "human" because even though Americans like to identify themselves as particular friends of the underdog, you can find a little of it everywhere. Anyone who's watched anime knows the Japanese have it. Anyone who's read the Bible knows the Israelites had it (no one was rooting for Goliath!) From mythology to literature to politics to sports, it keeps coming up.