The majority have one or more of the following flaws: uneducated, ignorant, prone to magical thinking, easily swayed by appeals to emotion without regard to the facts and a lack empathy for people not entirely like themselves.
Majority rule is NOT ideal.
That's true of any system of government. There isn't any really reliable way to pick good people. The best we can hope for is making sure that people have to cooperate to get anything done, and that means distributing power as widely as possible.
Distributing power as widely as possible results in a situation where the voice of the minority on any given subject will automatically never matter.
Racial integration would never have happened. Womens rights would never be recognized.
Sometimes you need to have someone who can make the right choice, no matter how unpopular it is.
Who gets to decide who's making the right choice? The person making the right choice, of course.
I never bought this argument. Racial integration happened because there were enough people in areas affected by it that knew things were wrong, and were willing to submit on a large enough scale to an authority that held their position. How do I know? We still have integration issues in my hometown, despite Our Benevolent Leader saying that it was wrong so many decades ago.
Women's rights happened because strong women stood up and pointed out that they were half of the damned population, so why should they be treated as inferiors? We still have women's rights issues, despite fairly clear laws saying that we should probably stop treating them as inferiors.
There are places that still resist both, and in those places there is clear dissent behind a backdrop of status-quo fear and stigma. Breaking through that stigma and encouraging people to speak their minds is where change happens. People are generally rational, but their rationality is affected by the need for stability, their fear of change and the unknown.
If you turn the argument on its head, and have an authority that's trying to fight common sense against the will of the people, you don't lose your common sense and eagerly submit to an ostensibly wiser leadership, you fight it as much as you can, sometimes to the point that it means problems for yourself, because it's a break in trust.