Discussion:
In the system of "approval voting", each voter may vote for as many candidates as she wishes. If there are three candidates, a voter may vote for 1,2, or 3 candidates. The winner is the candidate receiving the most votes (listed on the ballots of the most citizens). Each voter has strict preferences over the candidates (such as preferring candidate 3 to candidate 2 to candidate 1, with no indifference).
A) Show that any action that includes a vote for one's least preferred candidate is weakly dominated.
B) Show that any action that does not include a vote for one's most preferred candidate is weakly dominated.
C) Suppose voter A prefers candidate 1 to 2 to 3 to 4 (where there are 4 candidates). Show that all actions that consist of voting for up to three candidates and not skipping a lower numbered candidate are not weakly dominated (voting for 1 only, voting for 1 and 2, or voting for 1,2, and 3 are not weakly dominated.
Please use payoff matricies to illustrate the answers.