That problem you describe would be a political issue within a state. What Connecticut needs may be quite different from what Iowa needs. It is not relevant to national elections for president and vice president.
Where in the US Constitution does it say the minority rules? Same question for the state constitutions.
To paraphrase Trell, 1 person = 1 vote. The original articles of the US Constitution didn't say that outright, but the overwhelming trend of amendments and federal court decisions since 1792 have been in that direction.