Assignment:
A committee comprised of 15 members is called upon to rank three colors: red, blue, and yellow, from most preferred to least preferred. The committee members simultaneously announce their strict preference relations over the three colors. If red is the preferred color of at least five members of the committee, red is determined to be the prettiest color. Otherwise, if blue is the preferred color of at least five members of the committee, blue is determined to be the prettiest color. Otherwise, yellow is determined to be the prettiest color. Once the prettiest color is determined, the remaining two colors are then ranked by the simple majority rule.
(a) Is the social welfare function described here dictatorial? Justify your answer.
(b) Does the social welfare function described here satisfy the unanimity property? Justify your answer.
(c) Does the social welfare function described here satisfy the independence ofirrelevant alternatives property? Justify your answers.
Provide complete and step by step solution for the question and show calculations and use formulas.