The phrase "majority support" means that more than half of the people involved or affected agree with or are in favor of a particular idea, decision, or action. Full definition
But many surveys show majority support for climate policies based on other, wide - ranging preferences, such as energy independence, security, competitiveness, and the like. (dotearth.blogs.nytimes.com)
It couldn't get majority support of the membership. (judithcurry.com)
In other words, shareholders would follow a common procedure to vote «for» or «against» a candidate, and only those candidates who receive majority support would serve as directors. (businesslawblogsite.com)