The rich and poor alike get exactly one vote each. That is the cornerstone of a democracy. Of course, almost all political matters in the US are decided not via a democracy but via a representative democracy (most notable exceptions being initiatives in those jurisdictions that have them).
If the poor choose not to vote or understand who/what they are voting for, that's hardly the fault of successful people.
If a voter is swayed by political advertising (which, generally, does cost money, some of which comes from the "super rich"), they are an uninformed voter. Would they be more informed if the U.S. could figure out how to ban all political advertising? I don't think so since no one is forced to view, listen to, or read political ads any more than they are forced to view, listen to, or read ads for iPhones (and, in the case of TV and radio, the political ads seem to simply replace ads for consumer bling during "high season") - thus, political ads don't take away the opportunity for voters to inform themselves.