Final answer:
The Supreme Court case that involved the "one person, one vote" principle was Reynolds v. Sims, a 1964 decision that led to the restructuring of electoral districts so that each person's vote was equal in weight.
Step-by-step explanation:
The Supreme Court case that involved the principle of "one person, one vote" was Reynolds v. Sims, decided in 1964. This landmark decision played a pivotal role in reshaping the electoral map to ensure that every individual's vote has equal weight. Prior to this case, the inequitable population distribution across electoral districts meant that sparsely populated rural areas had disproportionate voting power compared to densely populated urban areas.
The Reynolds v. Sims ruling mandated that electoral districts be redrawn to contain approximately equal numbers of voters, thereby reinforcing the democratic principle that each vote should have the same value in determining the outcome of elections.
Other important cases that reinforced the principle of equitable voting include Baker v. Carr, which led to the enforceability of equal representation in state legislatures, and Smith v. Allwright, which struck down racial discrimination in primary elections. Together, these decisions help safeguard the essentials of a democratic society by ensuring fair representation and preventing practices undermining the effectiveness of a citizen's vote.