If the majority wants to build a bridge, and a minority doesn't, well, the majority gets their say.
For one, this makes the most people (the "majority", nudge nudge) get what they want.
For another, if it all comes down to raw power struggle, i.e hitting each other, the majority will win anyway. Voting is a way to ensure you get the above effect without the blood.
Consider also that for different courses of action, what is a majority and what is a minority changes. You can be pro "more taxes" and a majority, and also pro "legalize marijuana" (and a minority at that --just an example, doesn't mean the maj/min it talks about is accurate).
It's about WHO choses what it's "the best".
The majority should choose, period.
Everything else is "I know better than other people what they SHOULD want".
Even if you "know better" by some objective criterium, it should not be up to you to decide.
Because government is about choosing what people WANT not what is BEST for them.