Paillier cryptosystem preserve ordering of sums for two integer sequences
Paillier is not order preserving, so in your algorithm $x_1+y_1$ IF and ONLY IF $x_1+y_1 &lt;= x_2+y_2 \dots$ simply does not work. You can't do the $\leq$ comparison.

Whether you have the same $r$ or not does not really matter, if we look at the encryption:

$E(m)= g^m r^n$ mod $n^2$

You could try to achieve that by fixing $r^n$ such that the product with $x$ doesn't surpass $n^2$ (and thus isn't reduced any further by the modulus), but that means you have to find $r$ so that $r^n$ is quite low, and then your entire security will go down in flames most likely.