NZ Herald reported it understood that the council voted 7 to 4 in favour of the wage increase.
Of the other city councillors who responded, Angela O'Leary and James Casson voted against the pay rise along with MacPherson and Henry.
Hamilton News attempted to contact all the councillors to ask how they voted. Philip Yeung is currently absent.
Councillor Leo Tooman said he was absent with sickness from the debate and felt it was not his place to comment on the matter.
O'Leary believed it wasn't affordable to increase the CEO's pay at the current time.
"People are struggling so it's not the right thing to do at this time," O'Leary said.
Casson campaigned originally against the last pay rise and believed the money could be used differently despite backing Briggs.
"No reflection on Richard, I think he is a good guy and doing a good job."
One councillor in favour of the increase was deputy mayor Martin Gallagher.
Gallagher outlined the rate of Hamilton's development as a reason for supporting the pay rise.
"We have huge infrastructure challenges in the years ahead, we need to maintain and have the best and the brightest CEO and senior staff and staff in general," Gallagher said.
Rob Pascoe declined to comment on which way he voted but was happy with the result.
"What my personal vote is I don't think relevant at all," Pascoe said.
"I'm happy with the fact that the majority voted in favour, and that's where I think it should lie," he said.
Garry Mallett said he believed the pay rise was deserved by Briggs.
"He started off at a lower rate when we first employed him right at the start, so there is an element of catch-up there," Mallett said.
