One of the most compelling "arguments" are vivid, personal stories highlighted by anti-vaccination activists like Jenny McCarthy. It's a classic case of science versus anecdote.
Statistics and authoritative, impersonal medical information will never be as compelling as an emotional, tearful story told by a mother holding the daughter whose autism she blames on the vaccine.
VIDEO: The Evolution of Throwing
All the facts, data and research fades away under the glare of human emotion and faith.
As Eugenie Scott notes, "The people who do best in these debates are those who establish rapport with the audience, and who come across as trustworthy and believable. Affect is all; content is secondary. Which is another reason why formal debate is not the way to educate people about evolution or science in general."
Changing minds is unlikely. At best, Bill Nye may be able to - once again - debunk some long-discredited creationist canards, such as that evolution cannot explain the development of the human eye (it can), or that humans are descended from apes (we're not descended from them, instead we share a common ancestry).