A year's free council tax is up for grabs as part of a consultation exercise to find out voters' views.
Brighton and Hove Council is offering the prize of a year with no council tax to persuade people to have a say about the way they are governed.
People in Brighton and Hove will be able to say whether they want a directly elected mayor.
The system could be similar to London, where Ken Livingstone was voted mayor in May this year.
The mayor could nominate his own Cabinet of councillors or work with a council manager.
Or instead of a mayor, the council could opt for a council leader and Cabinet, similar to the current system.
A questionnaire is included on page nine of this month's Brighton and Hove News, which is delivered to homes.
All entries will be entered into a prize draw for the chance to win a year's free council tax. The winner will be announced some time in the next couple of months.
A council spokeswoman said: "We expect thousands of responses from local people so we should have a very good representation of different opinions."
A referendum on the issue is likely to take place next October.
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