It seeks for the referendums to be held concurrent with the Otumoetai/Pyes Pa byelection on February 17. The rubbish referendum is suggested as non-binding.
The council voted in August to introduce a rates-funded rubbish service - rather than pay-as-you-throw - from next year, and add a Māori ward in time for the local government elections in 2022.
Councillors Robson, Hollis and Morris were among those who voted against a Māori ward. Councillor Kiddie abstained. All four councillors also voted against the kerbside collection decision.
STV - single transferable vote - was introduced by the previous council prior to the 2019 election.
Hollis told the Bay of Plenty Times the February byelection, prompted by the recent resignation of councillor Jako Abrie, presented an opportunity to engage the community on two important issues he had heard a lot of feedback on.
"If the by-election wasn't going ahead we wouldn't bother, to be honest."
Hollis said democracy meant the decisions made by elected members should represent the views of the community and, in his opinion, the two decisions went against that. This was part of the motivation behind the proposal, he said.
"We think those decisions were wrong," Hollis said.
"We had people in the community that didn't know what was going on [regarding the kerbside scheme] because we held meetings in public excluded."
Morris, who spearheaded the notice of motion, said he received a letter from the Pāpāmoa Residents and Ratepayers' Association requesting a referendum on kerbside collection and Māori ward decisions.
"The main issue for me is the kerbside rubbish collection. I think the community is really clambering to have their say in it."
Morris said he also heard from the Concerned Citizens Group, which has been running a petition over the past month to force a referendum on the issue of Māori wards.
Petition organiser Ken Evans told the Bay of Plenty Times this week 2260 signatures had been collected from supporters so far.
The valid signatures of 4742 voters must be collected before February 22 to trigger a public-initiated binding referendum on vetoing the council's decision, but the council could also decide to initiate the poll itself.
Morris said holding the ward referendum concurrently with the byelection and kerbside question "made sense" and potentially saved ratepayers $70,000 to $80,000 per referendum.
"Whatever you think about the issue, the reality is it seems that a referendum is coming."
However, Morris said he believed the decision on whether to initiate referendums will "come down to the wire".
Kiddie said the referendums would save the community a lot of money to bring something forward that seemed inevitable due to petitioning. She said the community should have been more involved originally.
"I'm saying we did a bad job consulting with the community on kerbside and Māori wards."
Robson said his support for the proposed referendums came from a desire for the council to be better engaged with the community, which he believed was lacking when the kerbside and Māori ward decisions were made.
Papamoa Residents and Ratepayers Association chairman Philip Brown said he was disappointed the proposed kerbside collection referendum would be non-binding.
"They could just ignore it completely. It's an exercise in futility."
Brown said he would rather the council delay or defer the decision of the referendums "until they sort out the Crown manager".
On Tuesday, an independent review and observation team, chaired by Peter Winder, presented a report critical of the council's governance and the behaviour of elected members, recommending the council ask the Local Government Minister to appoint a Crown manager to help it.
The council deferred a decision on how to respond to the recommendations to Friday.
The report highlighted and criticised the council's habit of relitigating issues that would "further undermine the credibility of the council as an institution and as a partner".
The report stated the notice of motion calling for referendums was a "clear example of ongoing relitigation of issues and the potential for a flip flop based on who can get the numbers on the day.
"Such relitigation of issues will further undermine the credibility of the council as an institution and as a partner."