Arrow's theorem proves that no voting procedure can meet certain conditions of both fairness and logic. In this note, Grant Hayden explores the ramifications of the theorem for qualitative vote dilution. After describing Arrow's argument, Mr. Hayden considers four democratic voting procedures the -- Condorcet method, the amendment procedure, the Borda count, and cumulative voting-in the light of the theorem. He then explores some of the theoretical and practical implications of the theorem. In the remainder of the note, Mr. Hayden discusses how well section 2 of the Voting Rights Act of 1965 and its judicial interpretation in Thornburg v. Gingles accord with the dictates of Arrow's theorem, ultimately concluding that the courts should consider the first two in the light of the theorem.
Stanford Law Review
Grant M. Hayden, Some Implications of Arrow’s Theorem for Voting Rights, 47 Stan. L. Rev. (1995).