Assignment:
Let A be a set of alternatives, and let P N be a strict preference profile. Alternative a ∈ A is termed the Condorcet winner if for every alternative b = a, more than half of the individuals rank a above b. A social choice function G satisfies the Condorcet criterion if for every strict preference profile P N for which there exists a Condorcet winner a, it chooses the Condorcet winner, i.e., G(P N ) = a holds.
(a) Does a Condorcet winner a exist for every strict preference profile P N ? Justify your answer.
(b) Which of the social choice functions described, satisfy the Condorcet criterion? Justify your answer.
Provide complete and step by step solution for the question and show calculations and use formulas.