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Reynolds v. Sims is a court case that said every person's vote should count the same in a state's legislature. This means that each district should have the same number of people, so each person's vote is equal. The case was brought by people in Alabama who said that the way their state counted votes was unfair because it was based on an old census. The court agreed that this was not fair and that everyone's vote should be equal.
Reynolds v. Sims is a Supreme Court case from 1964. It says that the Equal Protection Clause of the Fourteenth Amendment requires that seats in a state legislature be divided up so that each person's vote counts the same. This means that each district should have the same number of people in it, so that each person's vote is worth the same amount.
For example, let's say that there are two districts in a state. District A has 10,000 people, and District B has 5,000 people. If each district gets one representative, then the people in District A have less voting power than the people in District B. This is because each representative in District A represents more people than each representative in District B. Reynolds v. Sims says that this is not fair, and that each district should have the same number of people in it.
In the Reynolds v. Sims case, people in Jefferson County, Alabama sued the state because they felt that the way the state divided up its districts was not fair. The state was using data from the 1900 census to divide up its districts, even though the population had changed a lot since then. The Supreme Court agreed with the people in Jefferson County, and said that the state needed to divide up its districts in a way that was fair to everyone.