Why does paterson believe that the convention should not adopt proportional representation?

Because more populous state would have more rights.

Explanation:

Paterson believed that every state is an independent entity and has a right to make decision as every other. According to that, if the proportional representation was introduced those states with less inhabitants would have less rights. Still, his plan was rejected at the end.

i confess that there are several parts of this constitution which i do not at present approve, but i am not sure i shall never approve them: for having lived long, i have experienced many instances of being obliged by better information or fuller consideration, to change opinions even on important subjects, which i once thought right, but found to be otherwise. it is therefore that the older i grow, the more apt i am to doubt my own judgment, and to pay more respect to the judgment of others.

for this case we have the following equation:

we apply distributive property to the terms within parentheses.

subtracting 2 on both sides of the equation: