"In the system of “approval voting”, a citizen may vote for as many candidates as she wishes. If there are two candidates, say A and B, for example, a citizen may vote for neither candidate, for A, for B, or for both A and B. As before, the candidate who obtains the most votes wins. Show that if there are k candidates then for a citizen who prefers candidate 1 to candidate 2 to . . . to candidate k, the action that consists of votes for candidates 1 and k − 1 is not weakly dominated."
Quoted from " An introduction to game theory" by Osborne.
I am having trouble showing that an action that votes for both A and K-1 cannot be weakly dominated by any other strategy. My approach to doing this is to find a scenario where the utility gained by voting for both A and K-1 is strictly greater than the utility gained by any other action. That said, I haven't been able to find a situation like that. Or is my approach inappropriate?