Is there a way to set a rule so that the automatic responses from voting buttons are moved to a specific folder? Since the subject line changes depending on the vote, one cannot use the subject line as a filter when the voting options are customized to include several potential responses.

No, and it is not recommended to do this anyway as the responses are being processed in the Inbox. Why do you want to move them out of there in the first place?

You can set general tracking and moving/deleting options via:
File-> Options-> Mail-> Tracking