A few weeks after a primary election riddled with polling-day issues, Los Angeles County officials announced they’ve completed the first phase of a major planned overhaul of the county’s voting system. County Registrar-Recorder Dean Logan envisions a future system in which, instead of being directed to designated polling stations on a single Tuesday, voters will be able to choose from hundreds of voting centers around the county during a 10-day window leading up to election day. There, instead of marking their selections with pen and paper, they will enter their selections on touch-screen ballot-marking devices, print out a paper ballot to review their selections, and feed the ballot back into the machine to be stored and counted. The county began exploring a redesign of the system in 2009. In 2014, the county Board of Supervisors approved a $15-million contract with the Bay Area design firm IDEO. The planning and design process has cost $14 million to date, Logan said.