Answer:
Original: "People who break traffic rules should also have to pay large fees for protecting the safety of other drivers."
You can do: "To protect the safety of other drivers, people who break traffic rules should pay large fees."
Explanation:
Make sure it is known the main reason for your argument is to PROTECT other drivers. It is not just to punish the ones commiting wrong, it makes a stronger case when you let it be known first.
