The concept of One-person, One-vote was established to guarantee that no voter had more or less weight to their vote than any other voter. Approval Voting does not break this rule. Approval Voting is asking every voter to give a “Yes” or “No” for every candidate. Each voter has the same choices in front of them and regardless of how many people you approve of, you can guarantee your preferences are being represented equally.
In fact, Approval Voting isn’t much different than the local, at-large, elections we’re used to where voters are choosing more than one seat to be filled. Each voter has exactly the same amount of political power.