## In the system of approvalvoting each voter may vote for as many candidates as sh

In the system of approvalvoting each voter may vote for as many candidates as she wishes. If there are three candidates a voter may vote for 12 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 ones least preferred candidate is weakly dominated.B) Show that any action that does not include a vote for ones 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 12 and 3 are not weakly dominated.Please usepayoffmatricies to illustrate the answers.