An opponent of the city mayor idea says he is in favour of the system that would be used to elect one.
Councillor Paul Elgood, leader of the Lib Dem group on Brighton and Hove City Council, will vote No in next month's referendum on whether there should be a directly-elected mayor.
But he said: "Although Lib Dems have doubts about the mayoral system there is no doubt that the voting system for any possible election of mayor is fairer than any other on offer for local or national government.
"The second vote means for the first time there is a form of PR introduced in local elections.
"I am happy to give this my support because it means that whoever wins will command a majority of support from the electors.
"This is a healthy development and goes some way to countering the cynicism about our electoral system.
" Importantly, I believe it will also help to increase turnout by making sure that all votes count."
Lord Bassam of Brighton, from the Yes campaign, said: "I very much welcome the Lib Dems' support for the two-vote system to be used for electing the mayor.
"It enables the eventual winner to consider broadening the representation in the cabinet based on the range of support attracted beyond usual party boundaries.
"In the campaign for an elected mayor I don't think we and the Lib Dems are far apart. They oppose centralised power and like us favour strong community representation through the development of neighbourhood forums.
"In London they backed a mayor, and they, like we do, back fair votes for a fairer system."
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