Dominance solvable approval voting games

This work provides necessary and sufficient conditions for the dominance solvability of approval voting games. Our conditions are very simple since they depend just on the number of possible winners when voters play weakly undominated strategies. If there are at most two possible winners, then the game is dominance-solvable and the outcome coincides with the Condorcet winner. If every candidate is a possible winner, the game is not dominance-solvable. If none of the previous conditions holds, then the game need not be dominance-solvable, and the outcome need not coincide with the Condorcet winner.