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Wiktionary
approval voting

n. A voting system in which each voter approves as many candidates as he wishes, and the candidate most approved of wins.

Wikipedia
Approval voting

Approval voting is a single-winner voting method used for elections. Each voter may "approve" of (i.e., select) any number of candidates. The winner is the most-approved candidate.

Guy Ottewell first described the system in 1977. and also by Robert J. Weber, who coined the term "Approval Voting." It was more fully published in 1978 by political scientist Steven Brams and mathematician Peter Fishburn.