[1] (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in different head-to-head competitions.)
Any voting method that ends in a runoff passes the criterion, so long as all voters are able to express their preferences in that runoff i.e. STAR voting passes only when voters can always indicate their ranked preference in their scores; if there are more than 6 candidates, then this is impossible.
The ballots for Approval voting do not contain the information to identify the Condorcet loser.
Thus, Approval Voting cannot prevent the Condorcet loser from winning in some cases.
The following example shows that Approval voting violates the Condorcet loser criterion.
This example shows that Majority Judgment violates the Condorcet loser criterion.
This example shows that the Minimax method violates the Condorcet loser criterion.
Assume four candidates A, B, C and L with 9 voters with the following preferences: Since all preferences are strict rankings (no equals are present), all three Minimax methods (winning votes, margins and pairwise opposite) elect the same winners: Result: L loses against all other candidates and, thus, is Condorcet loser.
This example shows that Range voting violates the Condorcet loser criterion.
Assume two candidates A and L and 3 voters with the following opinions: The total scores would be: Hence, L is the Range voting winner.