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Under the system, two of the three male candidates secured the posts while none of the four girls who put themselves forward were chosen.
The school is facing a backlash from parents and female pupils who claimed that girls are being denied opportunities under the supposedly “progressive” policy.
Securing the posts can boost university applications and offer other opportunities such as public speaking.
East Renfrewshire Council, which runs the school, said the move away from head boys and girls was part of a national trend designed to “allow for greater equality”.
However, feminist campaigners claimed that the supposedly forward-thinking move would limit opportunities for female pupils while handing an advantage to boys.
Marion Calder, a director at the For Women Scotland campaign group, said: “There have been multiple studies which show that in this type of election, girls are perfectly willing to vote for boys but boys will typically only vote for other boys.
“This is yet another misplaced policy in the guise of equality which in reality leads to the erasure of females and denies girls opportunities.
“It is no wonder that parents are up in arms. This school and any others that have adopted this regressive change should immediately scrap it and return to a system that has served them well for decades.”
The school is currently in the process of applying for charter status from the controversial charity LGBT Youth Scotland, which advises against use of words such as boy and girl in classrooms.
The organisation advises schools that terms such as “head pupil” are “more inclusive” as alternatives may distress pupils who identify as transgender or non-binary.