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Athabasca University

Section 2: Arrow’s Impossibility Theorem

Key Learning Points

  • Examine both social welfare functions and social choice functions from a more formal perspective.
  • Define the most important properties that a “good” social welfare function would satisfy.
  • Examine Arrow’s Theorem.

Activities

  1. Read section 9.4 the textbook;
  2. Watch the following videos:
    1. Social Choice: Impossibility of Non-Paradoxical Social Welfare Functions
    2. Social Choice: Arrow’s Theorem
    3. Impossibility of Non-paradoxical Social Choice Functions
  3. Do the following exercise:

    An agent, i, entertains preferences over the alternatives in U, which are represented by a transitive and complete preference relation, ≳i. Transitivity requests that ai b and bi c imply ai c for all a, b, cU, and completeness requires that any pair of alternatives a, bU is comparable, i.e., it holds that either a ≳i b or bi a or both. A utility function u: U → ℝ is said to represent a preference relation on U if, for all a, bU, u(a) ≥ u(b) if and only if ab . Show that, when U is finite, a preference relation can be represented by a utility function if and only if it is it is transitive and complete.

Updated December 04 2020 by FST Course Production Staff