The phrase "to have a majority" means having more than half of a group or votes. It implies having the larger portion or control in a situation or decision-making process. Full definition
However, a small number of nodes have the majority of connections. (cam.ac.uk)
You have parties elect sending their reps to parliament regardless of whoever has majority in parliament; it doesn't matter. (ghanapoliticsonline.com)
As to the latter, currently, child support is based upon the net income of the party who does not have the majority of parenting time. (divorcemag.com)