Gibbard–Satterthwaite Theorem versus Arrow Theorem
Solution 1:
There is a rather intimate connection between the results.
The original proof of Alan Gibbard gave the Gibbard-Satterthwaite theorem as a corollary to Arrow's theorem.
Philip Reny provides parallel proofs of Arrow's theorem and a certain strengthening of the Gibbard-Satterthwaite theorem here: Arrow’s theorem and the Gibbard-Satterthwaite theorem: a unified approach