The modification in rules to allow unpaired men to propose their own choice girl cannot affect the algorithm of pairing outputs.
Step-by-step explanation:
As it is the 21st century, each and every woman knows her rights, good and bad. As men are only allowed to propose in this scenario, they can not compel women to be their partners. So it is totally up to women either proposed girl or woman goes to that man or not it is totally up to her. So this modification has no symbolic effect on the pairing algorithm.