How can this research be done, then? Since the two sentences mean entirely different things, obviously people will react differently to them - they are not interchangeable, they have specific and different meanings!
"I support the division..."
and
"I support dividing..."
mean entirely different things. The first one is passive and indicates that the speaker/author is outside of the decision to divide\ and possible outside of the area itself.
The second one is active and implies that the speaker is going to be involved in the dividing activity itself.
Obviously the words will get different reactions from people because they mean different things. Without additional tests to query what the population understood the sentence to mean, along with how they feel about it, would make sense.
But as it is, this is like finding out that people react differently to "let's use fire" vs "lets use a blanket". They are totally different things.