A significant number of downvotes are given to questions whose askers didn't first check Google. This seems to be closely related to downvotes from asking a question with duplicates in the "Related Questions" field. How about also showing Google's "I'm feeling lucky," or some other results, in the Related Questions to help out with that?
EDIT: to clarify, I'm not talking about questions with answers on Stack Overflow, but rather questions with easy solutions available via Google. Here's a question just like that: http://stackoverflow.com/questions/3809224/what-are-my-options-for-3d-plotting-in-python