A linear function on the symmetric group is is specified by an nxn matrix A, and its value at a permutation π is A(1,π(1)) + … + A(n,π(n)). Such functions arise naturally in Erdos-Ko-Rado theory on the symmetric group. What can we say about such functions if they are Boolean? What if they are only approximately Boolean?   Based on https://discreteanalysisjournal.com/article/30186-boolean-functions-on-s_n-which-are-nearly-linear