From the definition of "society", any society must make decisions that affect all of its members, otherwise they aren't a society, they're a collection of non-interacting individuals. From the definition of "decision", these decisions must be framed by an individual - we have yet to master mind-meld technologies. From the definition of "power", the people who make the decisions have the power.
Majority voting is a red-herring. The way that existing power structures operate today is to frame the terms of the decision: they define what the alternatives are. Take a look at who sponsors ballot initiatives in California: very often, you'll find that a process that's as close to direct democracy as you'll get in modern society was actually sponsored by a wealthy billionaire or corporation behind the scenes, and he has crafted both the legislation and the public messaging around the legislation to suit his interests. If the voting public is faced with two alternatives and option A enriches elite #1 at the expense of the public while option B enriches elite #2 at the expense of the public, you can't really say that the voters have power.