A special rule in the House for sequencing different amendments. If more than one version receives a majority of votes, the last one to win a majority prevails.
An excerpt from The American Congress explains:
“Special rules are highly flexible tools for tailoring floor action to individual bills. Amendments may be limited or prohibited. The order of voting on amendments may be structured. For example, the House frequently adopts a special rule called a king-of-the-hill rule. First used in 1982, a king-of-the-hill rule provides for a sequence of votes on alternative amendments, usually full substitutes for the bill. The last amendment to receive a majority wins, even if it receives fewer votes than some other amendment. This rule allows members to vote for more than one version of the legislation, which gives them freedom both to support a version that is easy to defend at home and to vote for the version preferred by their party’s leaders. Even more important, the procedure advantages the version voted on last, which is usually the proposal favored by the majority party leadership.”
Also see: Partisanship or Protection: Examining the King of the Hill Rule.