The most significant reason to simply just discard the argument that same-sex marriage will lead to polygamy or pedophilia is by asking has it had this effect in other nations where same-sex marriage is allowed. The answer is "no."
The argument is this:
If same sex marriage is permitted, polygamy and pedophilia are next.
Same sex marriage is permitted in [insert nation].
[Insert nation] now allows polygamy and pedophilia.
That argument doesn't hold up regardless of which nation that permits same-sex marriage is inserted above. It is completely and utterly fallacious and ignorant. Sorry, but it is.