Allow members of We the People to express disagreement with a petition by providing an "anti-sign this petition" function. Give the "anti-sign" function one-to-one utility with a signature on a petition, such that one signature and one anti-signature equates to no signature. Permit any petition to be signed or anti-signed only once.
This will allow the administration to gain true insight into the interest of the American People as to the redress of any particular grievance.