$\sum{x} \ge \sum{y}$ implies $\sum{x^2} \ge \sum{y^2}$

Question

For any two sets of n non-negative integers, $x_i$ and $y_i$, is the above true, and how can one prove it? It seems like it ought to be true. I think induction is probably the best way, so I probably just need help to prove that if $x_1+x_2 \ge y_1 + y_2$ then $x_1^2 + x_2^2 \ge y_1^2 + y_2^2$ which I can't seem to manage.

Answer 1

It's wrong.

$2+2+2\geq1+1+4$, but $2^2+2^2+2^2\geq1^2+1^2+4^2$ is wrong.