Let \(n\) be an odd positive integer, and let
\[
f:\{-1,1\}^n\to\{-1,1\}.
\]
Interpret \(x_i=1\) as voter \(i\) voting for candidate \(A\), and \(x_i=-1\) as voter \(i\) voting for candidate \(B\). The value \(f(x_1,\dots,x_n)\) is the choice.

Find all functions \(f\) satisfying the following properties:
1. Anonymity: for every permutation \(\sigma\in S_n\),
\[
f(x_1,\dots,x_n)=f(x_{\sigma(1)},\dots,x_{\sigma(n)}).
\]
2. Neutrality:
\[
f(-x_1,\dots,-x_n)=-f(x_1,\dots,x_n).
\]
3. Monotonicity: if \(x=(x_1,\dots,x_n)\) and \(y=(y_1,\dots,y_n)\) satisfy
\[
x_i\le y_i \qquad \text{for all } i=1,\dots,n,
\]
then
\[
f(x)\le f(y).
\]