Groucho Marx once said, “I’ll never join any club that would have me for a member.” Well, Groucho is not interested in joining your investment club, but Julie is. Your club has 10 members, and the procedure for admitting a new member is simple: Each person receives a ballot that has two options: (1) admit Julie and (2) do not admit Julie. Each person can check one of those two options or abstain by not submitting a ballot. For Julie to be admitted, she must receive at least six votes in favor of admittance. Letting m be the number of ballots submitted with option 1 checked, assume that your payoff function is
a. Prove that checking option 1 (admit Julie) is not a dominant strategy.
b. Prove that abstaining is a weakly dominated strategy.
c. Now suppose you’re tired at the end of the day, so that it is costly for you to attend the evening’s meeting to vote. By not showing up, you abstain from the vote. This is reflected in your payoff function having the form
Prove that abstaining is not a weakly dominated strategy.