Supervisors Steve Lavagnino and Salud Carbajal will author a ballot argument in favor of increasing the county’s hotel bed tax rate from 10 percent to 12.5 percent, a suggested hike going before voters in November. The board voted 4-1 in April to put the measure on the ballot. Hotels in the county’s unincorporated regions — with Montecito accounting for the bulk of the revenues raised — have used the 10 percent figure for 24 years, compared to other cities using 12 percent; the jump would mean an extra $1.9 million every year.