Social choice procedures are critical in determining the outcome of collective decision-making processes. One fundamental principle in evaluating these procedures is the “Independence of Irrelevant Alternatives” (IIA), which states that the ranking of options should not change when irrelevant alternatives are added or removed. In this essay, we will examine a new social choice procedure that combines Plurality Voting and Dictatorship and assess whether it satisfies the IIA criterion.
The new social choice procedure outlined here combines Plurality Voting with Dictatorship. The steps are as follows:
If Plurality Voting results in a single winner, that winner is declared the overall winner.
If Plurality Voting results in a tie (i.e., two or more options receive the same number of votes), Dictatorship comes into play. In this case, the first voter, regardless of their original vote, becomes the dictator, and their choice is considered the final outcome.
Assessing Independence of Irrelevant Alternatives:
To evaluate whether this new social choice procedure satisfies the IIA criterion, we need to examine whether changing voters’ preferences between two specific options (a and b) can alter the outcome when irrelevant alternatives are added or removed.
In this scenario, we will demonstrate that changing voters’ preferences between options a and b does not alter the outcome, even when irrelevant alternatives are introduced or removed.
Suppose the initial preferences are as follows:
Voter 1: a > b (First voter)
Voter 2: a > b
Voter 3: a > b
In this case, Plurality Voting results in a clear winner, which is option a, as it has the majority of votes. Now, let’s consider an irrelevant alternative:
Voter 4: c > a > b
Despite the introduction of the irrelevant alternative c, the outcome remains unchanged. Option a still has the majority of votes (3 out of 4), and it is declared the winner.
In this scenario, we will show that changing voters’ preferences between options a and b can indeed alter the outcome when irrelevant alternatives are added or removed.
Initial preferences:
Voter 1: a > b (First voter)
Voter 2: a > b
Voter 3: b > a
In this case, Plurality Voting results in a tie between options a and b, as both have two votes each. Now, let’s introduce an irrelevant alternative:
Voter 4: c > a > b
With the introduction of the irrelevant alternative c, Dictatorship comes into play, and Voter 1 (the first voter) becomes the dictator. If Voter 1 prefers option a, they can dictate that a wins, even though the tie existed before the introduction of the irrelevant alternative.
The new social choice procedure, which combines Plurality Voting and Dictatorship, does not satisfy the Independence of Irrelevant Alternatives (IIA) criterion. Changing voters’ preferences between options a and b can alter the outcome when irrelevant alternatives are introduced or removed, as demonstrated in Scenario 2. This lack of IIA compliance raises concerns about the fairness and consistency of this procedure in situations where irrelevant alternatives come into play.
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