Suppose a group is trying to decide between 3 alternatives: A, B, and C. Using s

Question

Suppose a group is trying to decide between 3 alternatives: A, B, and C. Using some voting rule the group ranks the three alternatives and we can see that they prefer alternative A over alternative B. Then, the group is presented the same three alternatives (A, B and C) as well as a 4th alternative D. The voters’ individual preferences have not changed. However when the voting rule is used to rank the four alternatives we find that the group prefers B over A. Tell me which of Arrow’s assumptions was violated and carefully explain why.

Explanation / Answer

Here Arrow's assumption of Independence of irrelevant alternatives (IIA) is violated. Because this assumption suggests that The social preference between x and y should depend only on the individual preferences between x and y, it will not change if there is a new alternative introduced. That means if the voter's preferences are unchanged then the outcome of the vote will remain unchanged.

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