 Labour lost 21 of its 48 seats to become Cardiff's second party |
Cardiff could be run by councillors from all parties on a new-style "management board". The Liberal Democrats, who became the biggest party in last week's local government elections, want to scrap the existing cabinet structure.
They have proposed that all four parties on the council have seats on the board, chaired by Lib Dem group leader Rodney Berman.
Leadership of the authority will remain in limbo until a decision.
 | What is the great advantage... to have one lot of councillors disagreeing with another lot of councillors?  |
The council's annual meeting was due to be held on Thursday, but it has been postponed for two weeks while the parties try to come to an agreement. Former leader Russell Goodway resigned leadership of the Labour group after the elections, and he has been replaced by Greg Owens.
Mr Owens' Labour group is now the second largest with 27 of the 75 seats. The Lib Dems hold 33, Conservatives 12 and Plaid Cymru three.
Under the Lib Dem plan, the former all-Labour cabinet would be replaced with a board on which all parties would be represented in proportion to their strength on the council.
'Inclusive and democratic'
In a 10-member board, that could mean the Lib Dems with four seats, Labour three, Tories two and Plaid one.
 Rodney Berman says a change would reflect voters' opinions |
Mr Berman, who has been re-elected as the city's Lib Dem leader, said the council would have to ask permission from the Welsh Assembly Government to change the structure. He said the council could not return under this system to the old committee method. But there could be committees, with relevant board members as members.
The management board system has already been adopted in three other areas of Wales - Gwynedd, Merthyr and Powys.
Mr Berman described it as a "more inclusive and democratic structure" to reflect the views of voters and a switch from "one-party rule by a dominant few members of a single-party cabinet".
"What is the great advantage to the people of Cardiff to have one lot of councillors disagreeing with another lot of councillors?" he asked.
"An opposition for the sake of opposition provides no particular advantage to anyone".
Mr Berman said the Conservatives and Plaid were willing to back the idea - although the Tories had ruled out a two-party coalition.
Labour group leader Greg Owens was not available for comment.