In the system of “approval voting”, a citizen may vote for as many candidates as
ID: 1191430 • Letter: I
Question
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.
(a) Show that any action that includes a vote for a citizen’s least preferred candidate is weakly dominated, as is any action that does not include a vote for her most preferred candidate.
(b) 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.
Explanation / Answer
Assume that there are n players who vote. We can use lists of 0’sand 1’s to represent players’ actions.The intuition underlying this part’s claim is very simple. If a player ap-proves his/her favorite candidate only, then such an action can enlargethe candidate’s advantage in the campaign by 1 approval (or decrease thedisadvantage by 1 approval). However, if the player does not approvehis/her favorite candidate, or approves his/her least preferred candidate,there is no way to enlarge his/her favorite candidate’s advantage or de-crease the disadvantage. Therefore, the latter two kinds of actions are weakly dominated by the rst action