 In this election scenario, \(k\)-Approval for \(k=1,2,3\) cannot guarantee that the Condorcet winner \(A\) is elected. The Approval ballot \((\{A\},\{B\}, \{A, C\})\) does elect the Condorcet winner. In fact, Brams (2008, Chapter 2) proves that if there is a unique Condorcet winner, then that candidate may be elected under approval voting (assuming that all voters vote sincerely: see Brams 2008, Chapter 2, for a discussion). Note that approval voting may also elect other candidates (perhaps even the Condorcet loser). Whether this flexibility of Approval Voting should be seen as a virtue or a vice is debated in Brams, Fishburn and Merrill 1988a, 1988b and Saari and van Newenhizen 1988a, 1988b. 