In 1998, Wilcox was selected as a delegate to the fourth Constitutional Convention, running on a "Safeguard the People" ticket. His mission at the Convention was to ensure that any modifications made to the Australian Constitution towards a Republic maintained the present checks and balances against Centralism and the power of the Executive and the Judiciary. He argued, "We have had a Constitution, rightly or wrongly, that has been significantly destabilised, a generation of young people ... who believe we have a bad Constitution, paradoxically, when it is in fact the best in the world."