Do Uber/Lyft drivers see how you rated them before they rate you?

No, there are mechanisms in place.

First of all, the drivers cannot see exactly how you rated them at all.  They only see the total ratings update on their profile. 

Some drivers may attempt to deduce the rating by looking at how the ratings were affected, but this is difficult as 1) users have several days to leave a rating, and 2) the rating will not be updated until the driver submits their passenger rating (Uber) or until the next day (Lyft).  Therefore, the driver has to have very few rides under their belt or rarely give rides in order to have any idea.

More specifically, both Uber and Lyft drivers, upon completion of the ride, are taken to the rider feedback screen.  They must (albeit there being exceptions) rate the rider before they can proceed and accept another ride.

So, the short answer is that drivers must rate you before you rate them (in most cases).  This is to make sure there are no retaliatory feedback from the drivers. 

Does that make you feel better?

UPDATE 6/2018: Lyft now allows drivers to edit the rider feedback/rating up until 24 hours after a completion of a ride..  This means Lyft drivers could potentially review the revenue statement, match it up with the passenger listings and rate each differently based on the tip amount.

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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC