Prime Minister Shigeru Ishiba’s decision to resign has opened the door for any number of possible successors to replace him.

Whoever wins the LDP presidential election on Oct. 4 will need to secure cooperation from the opposition to be elected prime minister. The newly elected prime minister will still be in charge of a minority government and forced to work with at least one major opposition party to pass legislation.

The LDP and its coalition partner, Komeito, hold 221 seats in the 465-seat Lower House — 12 seats shy of a majority. In the less-powerful Upper House, on the other hand, the two parties need only three seats for a majority.