Assignment:
A committee comprised of 15 members is called upon to choose the prettiest color: red, blue, or yellow. The committee members simultaneously announce their strict preference relations among these three colors. If red is the most-preferred color of at least one committee member, red is declared the prettiest color. Otherwise, if blue is the most-preferred color of at least one committee member, blue is declared the prettiest color. Otherwise, yellow is declared the prettiest color.
(a) Is the social choice function described above dictatorial? Justify your answer.
(b) Is the social choice function described above monotonic? Justify your answer.
(c) Is the social choice function described above manipulable? Justify your answer.
Provide complete and step by step solution for the question and show calculations and use formulas.