“Arrow’s theorem and the Gibbard-Satterthwaite theorem: a unified approach,” Phil Reny, 2001

Presents a straightforward proof of Arrow’s Theorem (any IIA, complete, Paretian social welfare function is dictatorial) in an interesting manner, with the proof side-by-side with a proof of Muller-Sattherthwaite (any IIA, monotonic social choice function is dictatorial). Muller-Sattherthwaite immediately implies the better known Gibbard-Sattherthwaite Theorem (in any non-dictatorial voting system where every candidate can win under some individual preferences, strategic voting is optimal); a simple proof of this link is in the paper as well.

http://home.uchicago.edu/~preny/papers/arrow-gibbard-satterthwaite.pdf

Advertisements

One thought on ““Arrow’s theorem and the Gibbard-Satterthwaite theorem: a unified approach,” Phil Reny, 2001

  1. […] 5) Among the more beautiful simplifications of Arrow’s proof is Phil Reny’s “side by side” proof of Arrow and Gibbard-Satterthwaite, where he shows just how related the underlying logic of […]

Comments are closed.

%d bloggers like this: