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A new induction proof of the Gibbard-Satterthwaite theorem

Sarvesh Bandhu and Rohit Kumar
2025
Working Paper No
720
Body

In this paper, we provide a new induction proof of the Gibbard–Satterthwaite theorem, where the induction argument builds on n = 1 rather than the existing proofs using n = 2. The provided proof is much shorter, and the arguments are very intuitive, which will be helpful in teaching and for beginners in this field.

Key words
Social choice function, dictator, Gibbard–Satterthwaite theorem, induction
WP No. 720.pdf (589.25 KB)

A new induction proof of the Gibbard-Satterthwaite theorem

Author(s) Name: Sarvesh Bandhu and Rohit Kumar, 2025
Working Paper No : 720
Abstract:

In this paper, we provide a new induction proof of the Gibbard–Satterthwaite theorem, where the induction argument builds on n = 1 rather than the existing proofs using n = 2. The provided proof is much shorter, and the arguments are very intuitive, which will be helpful in teaching and for beginners in this field.

Keywords: Social choice function, dictator, Gibbard–Satterthwaite theorem, induction
WP No. 720.pdf (589.25 KB)