It sounds so obvious it could not possibly need a court case. But until 1964, a single rural vote could carry forty times the weight of a city vote, and the Supreme Court had to step in to fix it.
One person, one vote is the principle that each citizen's vote should carry roughly equal weight, which means electoral districts must contain roughly equal numbers of people. A vote in one district should not count for more than a vote in another.
For most of American history it was violated wholesale. States drew legislative districts and then simply refused to redraw them as people moved to cities. By the 1960s, rural districts with a handful of voters had the same power as urban districts packed with hundreds of thousands. In Alabama, the ratio reached 41 to 1.
The Supreme Court intervened in a burst of rulings. Baker v. Carr in 1962 let federal courts hear these cases at all. Then in 1964, Reynolds v. Sims held that state legislative districts must be roughly equal in population, and Wesberry v. Sanders applied the same rule to congressional districts.
Chief Justice Earl Warren put it plainly in Reynolds: legislators represent people, not trees or acres. The Constitution, he wrote, knows no preferred class of voters. The whole point of a vote is that yours equals your neighbor's.