In the API documentation for the question type, it says that you can access, for a specific question, whether or not the authenticated user (in the private_info scope) upvoted/downvoted the question.
Is there any way to filter for questions based on this information? That is, given an authenticated user, I would like to fetch a list of the questions for which they have cast up/down votes.
No. Currently the users type does not return any private_info and neither does the user_timeline type return any voting information.
No other API method allows for detecting a user's vote history except one question at a time. You would have to fetch every single question and test the downvoted and the upvoted properties.
If you limited your search only to questions asked since the user's last visit you might be able to brute-force this for votes on new questions
(Even Stack Overflow only runs about 7.5K questions per day (Quota is 10K calls, max 100 Q's per call))
-- but I wouldn't recommend it.
And, you'd miss new votes on old, established questions.
Update: At least one script works around this and fetches voting history by scraping the:
/users/current/?tab=votes&sort=upvote/users/current/?tab=votes&sort=downvotepages.
