IDEA: Pay drivers for no accidents. Increase the award for the longer a driver goes accident-free.

Pay handsome rewards to drivers with no accidents. Publish the awards and dollars amounts for all drivers to see. If a driver has passed three years (i.e. three, four, five, ten, etc.) with no incidents (i.e. tickets, wrecks, etc.), consider giving him an incrementally larger bonus and make sure everyone sees the payout and knows how it is earned.  You may consider publishing a sheet that tells how many days a driver has gone without accidents or incidents and give small bonuses or earnings as they pass certain numbers of days or months or years.  Post it every month so they can see on the website how long they gone and how much more time they have before crossing a new prize point.