Final answer:
The Supreme Court decision in Obergefell v. Hodges was based on the 14th Amendment's Equal Protection and Due Process Clauses, affirming the right to marry for same-sex couples nationwide.
Step-by-step explanation:
The majority decision of the Supreme Court in Obergefell v. Hodges relied on the 14th Amendment's Equal Protection and Due Process Clauses. In a landmark decision, the court affirmed the right of same-sex couples to marry, stating that the Fourteenth Amendment requires states to both license a marriage between two people of the same sex and to recognize a same-sex marriage when their marriage was lawfully licensed and performed out-of-state.
By applying the Equal Protection Clause, the Supreme Court underscored that states should not deny any person within its jurisdiction the equal protection of the laws. Thus, same-sex couples could not be deprived of the right to marry, a right that had been granted to opposite-sex couples, thereby requiring state recognition of such unions nationwide.
The Due Process Clause was also central to the decision, protecting against arbitrary denial of life, liberty, or property outside the sanction of law, and within this context, the right to marry was deemed a fundamental liberty.