We introduce history-bound reelections. In their simple form, they consist in a “ score-replication rule.” Under such a rule, an incumbent has to match the highest vote share he or she has obtained in any previous election in order to be reelected. We develop a simple three-period model to examine score-replication rules. We show that suitable variants of such rules can improve welfare, as they reduce the tendency of reelected incumbents to indulge in their own preferences, and they ensure that able officeholders are reelected. Candidates might offer their own score-replication rule in campaigns. We outline how political competition may be affected by such new forms of elections. (JEL D72, D83)