Beyond Arrow: Revealing True Preferences

In this paper, we examine the existence of strict strategy-proof voting mechanisms. Using Arrow’s Impossibility Theorem we prove any rational social choice function that respects Pareto optimality, independence of irrelevant alternatives, and monotonicity must be dictatorial. Next, we use the Gibbard-Satterthwaite theorem to show that strategy-proof voting mechanisms are necessarily dictatorial. Then, we use the Gibbard-Satterthwaite correspondence theorem to establish a one-to-one correspondence between social choice functions under Arrow’s construction and voting mechanisms under Gibbard and Satterthwaite’s construction. Finally, we extend these results by considering other voting mechanisms and discussing Vickrey-Clarke-Groves mechanisms