Brighton and Hove residents are being asked what they want if they vote against having a directly-elected mayor later this year - and they could win £100.
A referendum on the issue is likely to be held in October.
Brighton and Hove City Council has introduced two fallback options if proposals for a directly-elected mayor are defeated.
They are the current experimental system of having a leader and a Cabinet or an improved version of the old committee system, abandoned two years ago.
Before the referendum, councillors are keen to canvass the opinion of the public and have invited readers of the civic newspaper City News to give their opinion on which alternative system they prefer.
The same choice will be offered to 1,000 members of the Citizens' Panel and 5,000 people chosen at random from the electoral register.
People are being asked to make their choices by May 11. Entries will be placed in a prize draw with a £100 prize.
All the council's proposals, including the preferred fallback option, must be sent to the Government by June 30.
Under the Local Government Act, the improved committee system, favoured by many councillors, cannot be put forward by large councils as a first choice.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article