In 1991, he was a member of the Estonian Constitutional Assembly, and in 1992, he ran as a presidential candidate against Arnold Rüütel (3rd President of the Republic of Estonia, 2001–2006), and Lennart Meri (2nd President of the Republic of Estonia, 1992–2001), who won the election. Taagepera came in third with 23% of the popular vote. Later Taagepera admitted that one of the reasons why he ran, despite having little chance to win, was to take away votes from Rüütel and thus help Meri rise to the presidency.