Which 1964 supreme court case decided that state legislative districts must be roughly equal in population?

The Reynolds case v. Sims .

Explanation:

In Reynolds case v. Sims, the supreme court determined that the electoral districts should have approximately the same number in the population.

This decision was taken because during the year 1961, while the vote was taking place for the distribution of the state legislature in Jefferson, the voters did not agree with the result of the voting. Because in a district, the population had a large higher percentage of people than others, that is, the distribution of the districts was disproportionate.

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