A secret recording has emerged on YouTube in which Missouri congresswoman Vicky Hartzler is seen comparing gay marriage to incest, paedophilia and allowing three-year-olds to drive.

Ms Hartzler, a member of the Tea Party, was addressing a conference of college students at the Eagle Forum Collegians Summit in Washington on Thursday. She said that if same-sex marriages were allowed, it would lead to paedophiles and polygamists also being allowed to marry.

In the uncovered footage, Ms Hartzler says “Well, think about it . . . if you just cared about somebody, have a committed relationship, why not allow one man and two women or three women to marry?

“There are a lot of people in this country that support polygamy. Why not? They’re committed to each other. Why should you care? Why not allow group marriage? There are people out there who want that.”

She continued: “Well, is that the best policy? Why not allow an uncle to marry his niece? Why not allow a 50-year-old man to marry a 12-year-old girl if they love each other and they’re committed? So pretty soon if you don’t set parameters, you don’t have any.

“We’re saying marriage is between a man and a woman. It’s not a right in the Constitution as far as that goes either. It’s not a right of anybody to have a three-year-old to be able to drive a car. The government has [to] set some parameters.”

The Eagle Forum promotes conservatism on college campuses. Its annual conference is attended by around 200 students.

Ms Hartzler deemed the conference a success, writing on Twitter afterwards: “Spoke to almost 200 college students today at the Eagle Forum Collegiate Leadership Conference. A great group of sharp enthusiastic leaders.”

Mrs Hartzler was elected in 2010 to represent Missouri’s 4th Congressional District. She is an evangelical Christian and staunch opponent of gay marriage.

She is also a spokesman for the Coalition to Protect Marriage in Missouri, which successfully campaigned to ban same-sex marriage in the state.