Question

Two candidates, A and B, vie for office. Each of an odd number of citizens may vote for either candidate. (Abstention is not possible.) The candidate who obtains the most votes wins. (Because the number of citizens is odd, a tie is impossible.) A majority of citizens prefer A to win than B to win. Show that a citizen’s voting for her less preferred candidate is weakly dominated by her voting for her favorite candidate.

Answer 1

Answer:-

# Players: The citizens

# Actions : Each player’s set of actions consists of voting for
A and voting for B.

# Preferences: All players are indifferent among all action
profiles in which a majority of players vote for A; all players
are also indifferent among all action profiles in which a
majority vote for B. Some players (a majority) prefer an
action profile of the first type to one of the second type,
and the others have the reverse preference.

so that a citizen’s voting for her less preferred candidate is
weakly dominated by her voting for her favorite candidate.