Sheffield City Council has launched a consultation on whether local people want their cabinet led by a council leader or a mayor.
As well the traditional means of consultation the council is accepting email and online submissions.
Local people are being told that because of amendements to the 2000 Local Government Act, they are essentially deciding who will have the power to choose and head the cabinet.
At present the council’s leadership system has all 84 councillors deciding who will be the leader and which other councillors will make up the cabinet.
Under the change, the members would only be able to decide who will be the leader.
A mayor, elected for a term of four years, would choose his or her Cabinet up to a maximum of nine Councillors.