|Question||Table 28.3: Borda Count Implies A Wins and C comes in Third
(d) Suppose I get to decide which projects will be considered by the group and the group allows me to use my discretion to eliminate projects that clearly do not have widespread support. Will I be able to manipulate the outcome of the Borda Count by strategically picking which projects to leave off?
B: Arrow??s Theorem tells us that any non-dictatorial social choice function must violate at least one of his remaining four axioms.
(a) Do you think the Borda Count violates Pareto Unanimity? What about Universal Domain or Rationality?
(b) In what way do your results from part A of the exercise tell us something about whether the Borda Count violates the Independence of Irrelevant Alternatives (IIA) axiom?
(c) Derive again the Borda Count ranking of the five projects in part A given the voter preferences as described.
(d) Suppose voter 4 changed his mind and now ranks B second and D fourth (rather than the other way around). Suppose further that voter 5 similarly switches the position of B and D in his preference ordering??and now ranks B third and D fourth. If a social choice function satisfies IIA, which social rankings cannot be affected by this change in preferences?
(e) How does the social ordering of the projects change under the Borda Count? Does the Borda Count violate IIA?