Problem 1: Noise stability and influence
(a) Consider the majority function Maj$_3$ : {$\pm$1}$^3 \to$ {$\pm$1}. Calculate its noise stability for $p = 0.9$ and its probability of
the Condorcet paradox.
(b) Consider the following voting function for $n = 6$
$f(x_1, x_2, x_3, x_4, x_5, x_6) = sgn(31x_1 + 31x_2 + 28x_3 + 21x_4 + 2x_5 + 2x_6)$.
Calculate Inf$_i$[f] for $1 \le i \le 6$.