A variant of the newer Reddit rating system (Wilson score confidence interval) would be a good way to attack this without the complexity of machine learning. Effectively, a statistical sampling over time that builds confidence that a particular driver's rating is accurate. This would work well with their 40 initial trips policy and you could then just cull those who you have strong confidence are poor drivers. Sigma bounds over the whole population of drivers would also tell you what a "reasonable" rating is which would float over time.
That would work, though it's less than ideal and machine learning, is pretty easy. The main advantage is you can get very accurate predictions on what the next rating will be, and you can easily add in more arbitrary data to make the predictions more accurate. This is the goal of ratings after all, to estimate the probability that a service will be good or bad.
