Polygamy and same-sex marriage are different issues and one has nothing to do with the other. I stand by my position that anyone who believes polygamy would naturally follow if same-sex marriage were allowed is an uninformed belief.
This is because, while there is ample evidence that polygamous and polyandrous marriages are socially problematic with increased incidences of abuse and neglect over monogamous marriages, there are no data to support the same charge for same-sex relationships and marriages. I might add, that there are plenty of geographic places where same-sex marriage has existed for at least one generation, so the data would be available.
Therefore, there is ample reason for society to allow same-sex marriage and not polygamous marriages. Therefore, to state that same-sex marriage would lead to polygamous relationships or pedophilia is an ignorant statement.