If the appointment is not confirmed by him within 60 days, the decision is left to the panel. Similar systems exist in more than 30 states.
The revised "Missouri Plan" won first-round House approval by an 82 to 72 vote during Tuesday's session with 20 Republicans and all but one Democrat voting against. If Cox's proposal is ultimately signed by the governor and ratified by Missouri voters, the selection panel would gain a fourth citizen-representative, who would be selected by the governor. The legislation would also increase the number of candidates submitted to the governor to four and allow the governor to reject the first list.
Judicial selections would also require Senate confirmation.
With Republicans dominating Missouri's upper chamber, various Democratic opponents to the proposal voiced concern that requiring Senate consent would inject partisan politics into a system designed to avoid that.
"In many, many years we have not have had a failure in selecting judges with this system," Rep. Chris Kelly, D-Columbia said. "The bill's supporters want a political judiciary, and that's all this bill does."
Cox, in turn, said it would limit secrecy in the process of choosing judges by making the names and professional background of all judicial candidates public.
"Right now it is a system controlled by a small group of people who want to create a status quo," he said. "Like other parts of government, selecting judges should be a more open process."
Kelly challenged Cox to name a "bad" state justice, saying there were none because the Missouri Plan has worked and isn't in need of change.
Other supporters praised the would-be constitutional amendment for its ability to hold judges -- who can dramatically change policies in the state -- accountable to public scrutiny.
"It just gives voters their right to have some say in the process," Rep. Mark Bruns, R-Jefferson City, said. "Citizens should know who their judges are and have confidence that they will do the right things."