Johnson said there's a more recent example of how such a system would work: last year's recall of state Sen. President Russell Pearce.
Under state law, recall elections are open to all. That resulted in a race between Pearce and fellow Republican Jerry Lewis, with Lewis outpolling Pearce.
Johnson said that election between the two Republicans was affected by the fact that both had to appeal not only to Republicans but to Democrats and independents.
"Even Russell Pearce began campaigning on education and economic development,' Johnson said.
"They began to try to appeal to those centrist issues that are important to most people.'