Question

Question 2. A group with 11 members needs to make a choice from three alternatives: A, B and C. The individual preferences are given by: 4 members strictly prefer A to C to B, 3 members strictly prefer B to C to A, 2 members strictly prefer B to A to C, and 2 members strictly prefer C to A to B. (i) Is the individual preference profile single-peaked? Justify your answer. (ii) What is the social preference according to plurality rule? (iii) What is the social preference according to simple majority rule?

Answer 1

Option No. of votes А 4 В 2 C 1. Yes. The individual preference profile is single - peaked. Because individuals here have an outcome which is preferred the most compared to other alternatives and those outcomes which are further away from this most preferred option are less preferred. 2. Social preference according to plurality rule is B. This is because, B got more number of votes that is 5 votes 3. None of these options can be considered as a winner in the case of majority rule. Because, the total number of votes is 11. For simple majority, therefore one needs 6 votes. None of these options got more than 5 votes hence no winner as per the simple majority rule